Spatial variability and uncertainty in soils and their implication to slope stability and landslides

The field of geotechnical engineering has witnessed a significant increase in the application of random fields and spatial variability analyses, notably in slope stability assessments, with the aim of deepening our understanding of soil behaviour through realistic variability incorporation. However, the accurate modelling of real-world scenarios, such as random fields in slopes, presents substantial challenges, even with the adoption of simpler deterministic approaches. Both deterministic and probabilistic modelling methods inherently possess uncertainties and risks stemming from computational methods, human errors, sampling variability, equipment inaccuracies, temporal variations, and the intrinsically uncertain nature of soils. To comprehensively address and manage these challenges, a holistic approach becomes imperative. This involves meticulous site investigation, a profound grasp of soil uncertainties, robust modelling techniques, and a comprehensive understanding of the inherently uncertain nature of soils. The combination of these factors frequently produces probabilistic solutions, divergent from deterministic ones, consequently presenting distinct challenges. This thesis aims to delve into the expanding domain of random fields in soils, investigating the implications of spatial variability in soil strength on slope stability and landslide analyses. Firstly, this research tackles a significant challenge related to soil variability by focusing on Cone Penetration Test (CPT) data. Prior to this study, the comprehension of Correlation Length (CL) based on site-specific data was limited, with prevalent assumptions of deterministic CL in publications and commercial software. Through a comparative analysis of CPT data from cohesive soils (Alluvium) and granular soils (Crag deposits), this study establishes that CL can indeed be probabilistic, influenced by factors such as organic content, groundwater pressure, and abrupt changes in soil type. Furthermore, the research explores diverse approaches for calculating correlation lengths and, leveraging the probabilistic nature of CL, and proposes a Bayesian approach employing modern Bayesian inference techniques like Transitional Ensemble Markov Chain Monte Carlo (TEMCMC). The study also delves into multiple methods for generating random fields, emphasising the Karhunen-Lóeve (KL) and Fast Fourier Transform (FFT) approaches. While KL is integrated with Finite Element Limit Analysis (FELA) for granular slope stability analysis, FFT is applied to advance the Nodal-Integration based Particle Finite Element Method (NPFEM), specifically for spatial variability considerations. A notable contribution is introduced through the proposed Random Nodal-Integration based Particle Finite Element Method (RNPFEM) (Random Nodal-integration based Particle Finite Element Method), accommodating large-scale deformation problems. The NPFEM formulation had already been developed by others (Zhang, et al., 2023; Zhang, et al., 2022). However, the difficulties in implementing the RNPFEM revolve around the coupling of the NPFEM with not just a fast and efficient algorithm but also an approach where the mesh generation method of the NPFEM method is compatible with the mesh generation method for the random field. Compatibility in this sense referred to an approach where the random mesh generation method could be checked for the accuracy of the generated random field. This required generation of the field in a square mesh, mapping the random field to the slope area and undertaking checks of input versus output parameters. Indeed, checks are presented where it is shown that the statistical input parameters tend to the output parameters with mesh accuracy. Demonstrative simulations are conducted to scrutinise landslide runout distance and the behaviour of Alluvium in the post-failure process using the RNPFEM, marking a significant step forward in the field

Random field failure and post-failure analyses of vertical slopes in soft clays

This research investigates the spatial heterogeneity of cohesion within soft clay and its implications for slope stability and post-failure analysis. In-situ cone penetration tests were conducted in alluvial soft clays to calibrate probabilistic strength properties. Slope stability analyses employed deterministic, semi-deterministic, and comprehensive probabilistic approaches, while post-failure analysis utilised the nodal integration-based particle finite element method. The undrained shear strength (cu) demonstrated a log-normal distribution (mean: 19 kPa, standard deviation: 3 kPa), with correlation lengths modeled through Bayesian inference. Treating correlation lengths as distributions resulted in a negligible 2% difference compared to using a single value for the probability of failure. Semi-deterministic analyses exhibited results similar to probabilistic analyses, offering computational advantages. Nevertheless, probabilistic analysis, considering spatial variability, provided more comprehensive insights for post-failure analysis. For a vertical slope of critical height in the studied soft clay, probabilistic analyses predicted a range of runout distances from 0 m to over 125 m. Specifically, 89% of these distances were less than 80 m, and 82% were less than 40 m. The findings contribute to an enhanced understanding of spatial variations in soil strength within soft clay slopes, providing valuable insights for future geotechnical assessments and design considerations

Random field failure and post-failure analyses of vertical slopes in soft clays

This research investigates the spatial heterogeneity of cohesion within soft clay and its implications for slope stability and post-failure analysis. In-situ cone penetration tests were conducted in alluvial soft clays to calibrate probabilistic strength properties. Slope stability analyses employed deterministic, semi-deterministic, and comprehensive probabilistic approaches, while post-failure analysis utilised the nodal integration-based particle finite element method. The undrained shear strength (cu) demonstrated a log-normal distribution (mean: 19 kPa, standard deviation: 3 kPa), with correlation lengths modeled through Bayesian inference. Treating correlation lengths as distributions resulted in a negligible 2% difference compared to using a single value for the probability of failure. Semi-deterministic analyses exhibited results similar to probabilistic analyses, offering computational advantages. Nevertheless, probabilistic analysis, considering spatial variability, provided more comprehensive insights for post-failure analysis. For a vertical slope of critical height in the studied soft clay, probabilistic analyses predicted a range of runout distances from 0 m to over 125 m. Specifically, 89% of these distances were less than 80 m, and 82% were less than 40 m. The findings contribute to an enhanced understanding of spatial variations in soil strength within soft clay slopes, providing valuable insights for future geotechnical assessments and design considerations

Spatial variability characteristics of the effective friction angle of Crag deposits and its effects on slope stability

This study investigated the spatial variability characteristics of the effective friction angle of Crag deposits which are granular soils occur in the east of England. Cone Penetration Test data were obtained at 26 locations and interpreted statistically. The distribution characteristic of the effective friction angle of Crag deposits was derived with the mean value, the standard deviation and the correlation length calibrated. Illustrations were also shown on how factors such as ground water pressures and the existence of soft/organic soil zones affect the measurement of the autocovariance function and thus the correlation length. Bayesian inference technique was adopted alongside the method of moments to determine the correlation length. Based on the obtained statistical parameters, both semi-deterministic (based on standard geotechnical design codes) and probabilistic finite element limit analyses were carried out to investigate the stability of slopes in Crag deposits. Slopes of various inclined angles were considered and comparisons between the semi-deterministic and probabilistic results were conducted to improve the understanding of the stability of Crag slopes and to provide insight into the slope stability code used in practice