DV
D. Varkey
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1
The stability of six regional dyke cross-sections in the Netherlands was re-assessed using the random finite element method (RFEM), which explicitly accounts for the spatial variability of strength parameters. The RFEM assessments of the cross-sections were shown to result in significantly narrower response distributions than those obtained by ignoring the spatial variability, and therefore would result in more economical designs. Given the complexity of RFEM for applications in daily engineering practice, the results obtained from the re-assessments of the six dyke cross-sections were used to propose partial factors that can be used in practice to achieve the desired reliability levels for regional dykes. When applied in a conventional semi-probabilistic assessment of a dyke cross-section, these partial factors would result in the same level of reliability as would have been obtained by carrying out an RFEM analysis of the same cross-section.
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The stability of six regional dyke cross-sections in the Netherlands was re-assessed using the random finite element method (RFEM), which explicitly accounts for the spatial variability of strength parameters. The RFEM assessments of the cross-sections were shown to result in significantly narrower response distributions than those obtained by ignoring the spatial variability, and therefore would result in more economical designs. Given the complexity of RFEM for applications in daily engineering practice, the results obtained from the re-assessments of the six dyke cross-sections were used to propose partial factors that can be used in practice to achieve the desired reliability levels for regional dykes. When applied in a conventional semi-probabilistic assessment of a dyke cross-section, these partial factors would result in the same level of reliability as would have been obtained by carrying out an RFEM analysis of the same cross-section.
Free-field site response analysis is a standard technique used to predict soil deposit dynamic response and liquefaction susceptibility. Such analyses are typically carried out by implementing periodic boundaries to guarantee the same speed of the dynamic waves travelling across them. However, when using random fields to consider the impact of soil spatial variability there is the possibility of an inconsistency with periodic boundaries. This is due to the generation of non-identical properties at the lateral boundaries on using traditional random fields. To overcome this inconsistency, this paper proposes periodic random fields to model spatial variability by matching the periodicity at the boundaries. To investigate the significance of using the proposed approach, a heterogeneous soil deposit subjected to earthquake loading is analysed using the random finite element method. The results show that, for certain values of the horizontal scale of fluctuation, ensuring consistency at the lateral boundaries could result in less conservative predictions of the extent of the liquefied areas.
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Free-field site response analysis is a standard technique used to predict soil deposit dynamic response and liquefaction susceptibility. Such analyses are typically carried out by implementing periodic boundaries to guarantee the same speed of the dynamic waves travelling across them. However, when using random fields to consider the impact of soil spatial variability there is the possibility of an inconsistency with periodic boundaries. This is due to the generation of non-identical properties at the lateral boundaries on using traditional random fields. To overcome this inconsistency, this paper proposes periodic random fields to model spatial variability by matching the periodicity at the boundaries. To investigate the significance of using the proposed approach, a heterogeneous soil deposit subjected to earthquake loading is analysed using the random finite element method. The results show that, for certain values of the horizontal scale of fluctuation, ensuring consistency at the lateral boundaries could result in less conservative predictions of the extent of the liquefied areas.
Conference paper
(2023)
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Divya Varkey, Abraham P. van den Eijnden, Michael A. Hicks
Geological uncertainty can significantly influence the computed response of a geotechnical structure. For example, ignoring the presence of a weak soil layer embedded within a stronger layer and assuming a deterministic stratigraphic boundary can significantly underestimate the probability of failure. In this paper, the coupled Markov chain method has been used for modelling this form of uncertainty. A strategy for estimating the horizontal transition probability matrix with limited data has been proposed, which is one of the biggest challenges with using this method. In particular, different sampling intervals in the vertical and horizontal directions have been considered in estimating the matrix for simulating realistic field situations. The applicability of the proposed method has been demonstrated using a set of CPTs in the Netherlands. The results highlight a problem that arises due to the coupling algorithm used in this method.
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Geological uncertainty can significantly influence the computed response of a geotechnical structure. For example, ignoring the presence of a weak soil layer embedded within a stronger layer and assuming a deterministic stratigraphic boundary can significantly underestimate the probability of failure. In this paper, the coupled Markov chain method has been used for modelling this form of uncertainty. A strategy for estimating the horizontal transition probability matrix with limited data has been proposed, which is one of the biggest challenges with using this method. In particular, different sampling intervals in the vertical and horizontal directions have been considered in estimating the matrix for simulating realistic field situations. The applicability of the proposed method has been demonstrated using a set of CPTs in the Netherlands. The results highlight a problem that arises due to the coupling algorithm used in this method.
Uncertainty is inevitable in the characterisation of a geotechnical site, especially due to the inherently heterogeneous nature of the ground. In this paper, a method for characterising a subsurface with limited cone penetration test (CPT) data is proposed. The method is based on integrating predictions of CPT parameters with a probabilistic approach for subsoil classification at the CPTs. The predicted stratigraphy is able to capture the spatial variability of soil measured via CPTs and takes account of the uncertainties that arise from transforming CPT measurements into soil units as well as errors in the measurements themselves. The applicability of the proposed method is demonstrated for a site in the Netherlands. The results show that the proposed approach can identify the most likely classification in the domain with good accuracy. Furthermore, the significance of considering the uncertainties in predicting the most likely classification is illustrated via finite element stability analyses of a slope cut-out in the domain.
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Uncertainty is inevitable in the characterisation of a geotechnical site, especially due to the inherently heterogeneous nature of the ground. In this paper, a method for characterising a subsurface with limited cone penetration test (CPT) data is proposed. The method is based on integrating predictions of CPT parameters with a probabilistic approach for subsoil classification at the CPTs. The predicted stratigraphy is able to capture the spatial variability of soil measured via CPTs and takes account of the uncertainties that arise from transforming CPT measurements into soil units as well as errors in the measurements themselves. The applicability of the proposed method is demonstrated for a site in the Netherlands. The results show that the proposed approach can identify the most likely classification in the domain with good accuracy. Furthermore, the significance of considering the uncertainties in predicting the most likely classification is illustrated via finite element stability analyses of a slope cut-out in the domain.
Conference paper
(2023)
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Beiyang Yu, Divya Varkey, Abraham P. van den Eijnden, Guillaume Rongier, Michael A. Hicks
This research focuses on investigating the relative performance of a range of machine learning algorithms, namely the artificial neural network, support vector machine, Gaussian process regression, random forest, and XGBoost, for predicting the undrained shear strength from cone penetration test data. This is to assess how machine learning could help us lower the need for laboratory test data. The training dataset compiles 526 data from 12 regions and the testing dataset consists of 20 data from a polder located close to Leiden in the Netherlands. In addition, k-fold and group k-fold cross-validation strategies are both applied to validate the models. The poor performance of the models during group k-fold cross-validation suggests that, while machine learning techniques can perform well when site-specific data are included during training, they struggle to generalize without site-specific data. This highlights the difficulty of capturing soil heterogeneity and suggests that either machine learning methods should be trained on specific sites for which some data are already available, or much larger training datasets are needed.
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This research focuses on investigating the relative performance of a range of machine learning algorithms, namely the artificial neural network, support vector machine, Gaussian process regression, random forest, and XGBoost, for predicting the undrained shear strength from cone penetration test data. This is to assess how machine learning could help us lower the need for laboratory test data. The training dataset compiles 526 data from 12 regions and the testing dataset consists of 20 data from a polder located close to Leiden in the Netherlands. In addition, k-fold and group k-fold cross-validation strategies are both applied to validate the models. The poor performance of the models during group k-fold cross-validation suggests that, while machine learning techniques can perform well when site-specific data are included during training, they struggle to generalize without site-specific data. This highlights the difficulty of capturing soil heterogeneity and suggests that either machine learning methods should be trained on specific sites for which some data are already available, or much larger training datasets are needed.
This paper investigates the influence of three forms of uncertainty on the probabilistic stability of an idealised 3D embankment slope. These are: 1D spatial variability in the external geometry of the slope along its length, 2D spatial variability in the depth of the boundary between the embankment material and the foundation layer, and 3D spatial variability in the shear strength properties of the slope and foundation materials. The relative influence of each uncertainty has been investigated using the random finite element method, based on statistics consistent with a Dutch regional dyke. The results indicate that, for such a structure, the soil spatial variability has a much greater influence than uncertainties relating to embankment geometry and inter-layer boundary. In particular, it is demonstrated that the spatial correlation of material properties along the length of the embankment has a greater influence on the probabilistic characteristics of the embankment slope stability and failure consequence than the spatial correlation of properties perpendicular to it. A worst case scale of fluctuation for the material properties is identified.
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This paper investigates the influence of three forms of uncertainty on the probabilistic stability of an idealised 3D embankment slope. These are: 1D spatial variability in the external geometry of the slope along its length, 2D spatial variability in the depth of the boundary between the embankment material and the foundation layer, and 3D spatial variability in the shear strength properties of the slope and foundation materials. The relative influence of each uncertainty has been investigated using the random finite element method, based on statistics consistent with a Dutch regional dyke. The results indicate that, for such a structure, the soil spatial variability has a much greater influence than uncertainties relating to embankment geometry and inter-layer boundary. In particular, it is demonstrated that the spatial correlation of material properties along the length of the embankment has a greater influence on the probabilistic characteristics of the embankment slope stability and failure consequence than the spatial correlation of properties perpendicular to it. A worst case scale of fluctuation for the material properties is identified.
Various simplified approaches are used to calculate the characteristic values of shear strength properties, which have then been used in deterministic stability analyses of a dyke cross-section. The calculated factors of safety are compared with the 5-percentile ‘system response’ of the dyke cross-section, calculated using the more exhaustive random finite-element method (RFEM), which is consistent with the requirements of Eurocode 7. The simplified methods accounting for variance reduction due to averaging of property values mostly give factors of safety within 10% of the RFEM solution, whereas the factor of safety based on the 5-percentile material properties is significantly over-conservative.
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Various simplified approaches are used to calculate the characteristic values of shear strength properties, which have then been used in deterministic stability analyses of a dyke cross-section. The calculated factors of safety are compared with the 5-percentile ‘system response’ of the dyke cross-section, calculated using the more exhaustive random finite-element method (RFEM), which is consistent with the requirements of Eurocode 7. The simplified methods accounting for variance reduction due to averaging of property values mostly give factors of safety within 10% of the RFEM solution, whereas the factor of safety based on the 5-percentile material properties is significantly over-conservative.
Doctoral thesis
(2020)
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Divya Varkey
This thesis utilises the random finite element method (RFEM) to provide practical guidance and tools for geotechnical engineers to account for the influence of soil spatial variability. This has involved: (a) practical insight and guidance on the choice of characteristic soil property values and scales of fluctuation; (b) a robust approach to reliability assessment and design that obviates the need for explicit calculation of characteristic values; and (c) the benchmarking and improving of simpler analysis tools.
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This thesis utilises the random finite element method (RFEM) to provide practical guidance and tools for geotechnical engineers to account for the influence of soil spatial variability. This has involved: (a) practical insight and guidance on the choice of characteristic soil property values and scales of fluctuation; (b) a robust approach to reliability assessment and design that obviates the need for explicit calculation of characteristic values; and (c) the benchmarking and improving of simpler analysis tools.
An improved semi-analytical method for calculating the reliability of 3D slopes with spatially varying shear strength parameters is proposed. The response of an existing semi-analytical method has been compared with that of the computationally more intensive, but more general, random finite element method (RFEM), demonstrating that the simpler method underestimates the failure probability. An alternative relationship for the expected failure length and two correction factors are proposed, which modify the original formulation of the simpler method. The proposed approach gives substantially improved results that compare favourably with those obtained by RFEM, and therefore provides a more accurate simplified solution.
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An improved semi-analytical method for calculating the reliability of 3D slopes with spatially varying shear strength parameters is proposed. The response of an existing semi-analytical method has been compared with that of the computationally more intensive, but more general, random finite element method (RFEM), demonstrating that the simpler method underestimates the failure probability. An alternative relationship for the expected failure length and two correction factors are proposed, which modify the original formulation of the simpler method. The proposed approach gives substantially improved results that compare favourably with those obtained by RFEM, and therefore provides a more accurate simplified solution.
Conference paper
(2019)
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Divya Varkey, Michael A. Hicks, Philip J. Vardon, Abraham P. van den Eijnden
The Dutch dyke network includes 14,000 km of regional dykes that are regularly assessed in order to reduce the risk of flooding. The current strategy for maintenance and/or upgrading of existing dykes is based on safety assessments using partial factors and reliability-based characteristic values of material properties, interpreted from Eurocode 7 (EC7). In this paper, an historic dyke in the Netherlands has been analysed for stability using two methods: (a) based only on the point statistics of the material properties, as is widely adopted in Dutch practice based on a simplified interpretation of EC7, and (b) based on both the point and spatial statistics of the material properties, using a probabilistic approach in line with the full requirements of EC7. The results of safety assessments by the two methods show that a consideration of the spatial variability leads to a narrower range of possible responses, and thereby to a higher computed factor of safety at the target reliability of 95%. Moreover, for the dyke section considered, it results in much reduced remedial action compared to that suggested as a consequence of using the simplified approach, and thereby to a more economic design and reduced environmental impact.
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The Dutch dyke network includes 14,000 km of regional dykes that are regularly assessed in order to reduce the risk of flooding. The current strategy for maintenance and/or upgrading of existing dykes is based on safety assessments using partial factors and reliability-based characteristic values of material properties, interpreted from Eurocode 7 (EC7). In this paper, an historic dyke in the Netherlands has been analysed for stability using two methods: (a) based only on the point statistics of the material properties, as is widely adopted in Dutch practice based on a simplified interpretation of EC7, and (b) based on both the point and spatial statistics of the material properties, using a probabilistic approach in line with the full requirements of EC7. The results of safety assessments by the two methods show that a consideration of the spatial variability leads to a narrower range of possible responses, and thereby to a higher computed factor of safety at the target reliability of 95%. Moreover, for the dyke section considered, it results in much reduced remedial action compared to that suggested as a consequence of using the simplified approach, and thereby to a more economic design and reduced environmental impact.
Conference paper
(2019)
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Divya Varkey, Michael Hicks, Phil Vardon
An improved method for the reliability analysis of 3D slopes has been proposed based on the semi-analytical method of Vanmarcke (1977). Comparing the predicted responses of an idealised 3D slope obtained by the more general, albeit computationally intensive, random finite element method (RFEM), and the original semi-analytical method showed that the latter gives unconservative estimates of the probability of failure. Three significant areas were identified as requiring improvement in the simpler method. These were corrected by: (i) a correction factor to reduce the overestimation of endresistance in 3D failures, i.e. reducing the impact of conservative geometric assumptions; (ii) a correction factor to correct for overestimating the average shear strength on the failure plane, which is found to be lower than the average shear strength for the entire slope; and (iii) an alternative relationship for the expected failure length for intermediate values of the spatial correlation length of the shear strength. The proposed modified semi-analytical method gives substantially improved results that are comparable to RFEM, while retaining the simplicity of the original method.
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An improved method for the reliability analysis of 3D slopes has been proposed based on the semi-analytical method of Vanmarcke (1977). Comparing the predicted responses of an idealised 3D slope obtained by the more general, albeit computationally intensive, random finite element method (RFEM), and the original semi-analytical method showed that the latter gives unconservative estimates of the probability of failure. Three significant areas were identified as requiring improvement in the simpler method. These were corrected by: (i) a correction factor to reduce the overestimation of endresistance in 3D failures, i.e. reducing the impact of conservative geometric assumptions; (ii) a correction factor to correct for overestimating the average shear strength on the failure plane, which is found to be lower than the average shear strength for the entire slope; and (iii) an alternative relationship for the expected failure length for intermediate values of the spatial correlation length of the shear strength. The proposed modified semi-analytical method gives substantially improved results that are comparable to RFEM, while retaining the simplicity of the original method.
Journal article
(2019)
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Michael A. Hicks, Divya Varkey, Abraham P. van den Eijnden, Tom de Gast, Philip J. Vardon
A case study involving the assessment and re-design of an existing dyke, founded on a layered soil, has compared deterministic analysis based on 5-percentile property values and a reliability-based random finite element analysis consistent with the requirements of Eurocode 7. The results show that a consideration of the spatial nature of soil variability generally leads to higher computed factors of safety and, for those dyke sections requiring remedial action, to more economic designs. Back-figured characteristic values are shown to be considerably higher than the 5-percentile soil properties; hence, a reduction in over-conservatism is achieved.
...
A case study involving the assessment and re-design of an existing dyke, founded on a layered soil, has compared deterministic analysis based on 5-percentile property values and a reliability-based random finite element analysis consistent with the requirements of Eurocode 7. The results show that a consideration of the spatial nature of soil variability generally leads to higher computed factors of safety and, for those dyke sections requiring remedial action, to more economic designs. Back-figured characteristic values are shown to be considerably higher than the 5-percentile soil properties; hence, a reduction in over-conservatism is achieved.
The paper investigates the stability of slopes with spatially variable and cross-correlated shear strength parameters in 3D. The influence of various cross-correlation coefficients between these parameters on the probability of 3D slope failure has been considered for different levels of anisotropy of the heterogeneity in the shear strength. Specifically, 3D random fields of cohesion and friction angle were generated using the Local Average Subdivision method, and these were correlated with each other by various degrees. The fields were then linked to finite element analyses within a Monte Carlo framework. The results indicate that a positive cross-correlation between the parameters reduces the slope reliability, whereas a negative cross-correlation between the parameters increases the reliability.
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The paper investigates the stability of slopes with spatially variable and cross-correlated shear strength parameters in 3D. The influence of various cross-correlation coefficients between these parameters on the probability of 3D slope failure has been considered for different levels of anisotropy of the heterogeneity in the shear strength. Specifically, 3D random fields of cohesion and friction angle were generated using the Local Average Subdivision method, and these were correlated with each other by various degrees. The fields were then linked to finite element analyses within a Monte Carlo framework. The results indicate that a positive cross-correlation between the parameters reduces the slope reliability, whereas a negative cross-correlation between the parameters increases the reliability.
A 3D slope stability problem with spatially varying shear strength parameters has been analysed using the 3D random finite element method. This method links random fields of the random variables, in this case, cohesion and friction angle, with the finite element method within a Monte Carlo framework. The influence of spatial variability on calculated factors of safety and failure consequence has been investigated, and the results compared with a simpler 3D solution proposed by Vanmarcke. The simpler approach predicted a lower probability of failure under certain conditions, although, at high levels of anisotropy of the heterogeneity, the solutions converged. The reasons for the different solutions have been evaluated
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A 3D slope stability problem with spatially varying shear strength parameters has been analysed using the 3D random finite element method. This method links random fields of the random variables, in this case, cohesion and friction angle, with the finite element method within a Monte Carlo framework. The influence of spatial variability on calculated factors of safety and failure consequence has been investigated, and the results compared with a simpler 3D solution proposed by Vanmarcke. The simpler approach predicted a lower probability of failure under certain conditions, although, at high levels of anisotropy of the heterogeneity, the solutions converged. The reasons for the different solutions have been evaluated