Geologic material properties of hillslopes are inherently heterogeneous, with complex layering structures due to geological deposition processes. Lacking detailed sampling of the properties’ spatial distribution has led to the stochastic representation of the properties to address uncertainty in the hillslope stability evaluation. This study treats the spatial distributions of the shear strength parameters, the cohesion (c), and the internal friction angle (φ), in a synthetic two-dimensional slope as stochastic random fields characterized by their means, variances, and correlation scales. This study then evaluates the cross-correlation between these parameters and the factor of safety (FS) using unconditional Monte Carlo simulation (MCS). Different from classical sensitivity analyses, the cross-correlation analysis of FS and the stochastic parameter fields stresses the importance of the orientation of the large-scale geological layering, the correlation between the geological media’s cohesion, and the internal friction angle at the local scale on the probability and uncertainty of failure of the heterogeneous hillslope. The analysis further guides the field sampling strategy to reduce uncertainty in the slope stability analysis due to unknown heterogeneity. More importantly, it suggests the location of stability reinforcement measures. The results of this study provide cost-effective tools for geoengineers to deal with field slope stability analysis under uncertainty.

For the characterization of heterogeneous aquifers, transient hydraulic tomography (THT) was proposed as a promising method to obtain the distribution of hydraulic parameters with satisfying spatial resolution using different approaches. These include hydraulic travel time, attenuation inversions, thermal tracer tomography, and geostatistical inversion with successive linear estimator (SLE). For the same hydrogeological test, different inversion methods tend to use different sub-data sets to obtain different hydraulic parameters. Up to now, however, few studies have focused on revealing the respective characteristics of these inversion methods and attempted to improve the accuracy of aquifer characterization by bridging the shortcomings of the inversion methods. The main objective of this study was to evaluate the utility of multiple inversion techniques on aquifer heterogeneity characterization. A series of warm water injection tests were first simulated in a fluvial aquifer analogue outcrop. The calculated head and temperature datasets from these tests were fully utilized to reveal the aquifer heterogeneity by using all of the four above-mentioned inversion methods. The results show that the thermal tracer tomography, hydraulic travel time, and attenuation tomography characterized the high permeability zones more accurately within the well area, whereas the geological statistical method tended to depict the overall distribution of $K$ values for a larger area. By comparison analysis and combinations of the individual inversion results, the scientific and economic complementarity can be studied and some valuable advice for the choice of different inversion methods can be recommended for future practices.

Due to large-scale geological deposition processes, slope structures are often stratified, which means that the spatial distribution of the parameters involved in slope reliability evaluation is statistically anisotropic. This paper studies the effect of the statistical anisotropy of undrained shear strength on the probability of slope failure (p_f) based on the Monte Carlo simulation. The results show that for the horizontally layered slope, the larger the horizontal correlation scale of undrained shear strength (λ_x) is, the larger p_f is, especially when λ_x is smaller than the slope length; for the vertically layered slope, the larger the vertical correlation scale (λ_y) is, the smaller p_f is, especially when λ_y is smaller than the slope height. Additionally, the mechanism of the above results is discussed by analyzing the displacement distribution at different correlation scales. The findings indicate that in the reliability evaluation of undrained slopes in stratified structures, either underestimation of λ_x or overestimation of λ_y leads to an unconservative estimate of p_f, resulting in an overestimation of the slope stability.

In the realm of groundwater science, characterization of heterogeneous aquifers is pivotal for resolving diverse groundwater resource and engineering-related problems that require the detailed spatial distribution of hydraulic parameters. As research progresses, one hydraulic tomographical method, which is based on hydraulic travel time inversion, emerges as a promising and rapid method due to its robust and efficient calculation. In the field, the acquisition of hydraulic excitation and head observation data required for inversion is less time-consuming. Data collection from a single hydraulic test (such as a pumping test) typically takes only a few minutes or even a few tens of seconds. However, the field application of this method faces challenges. Hydraulic travel time is typically generated in the early stages of hydrogeological tests (e.g., early drawdown of a pumping test), yet accurate data may not be readily available because of the noise signals from test equipment, which can contaminate travel time signals, leading to inaccurate inversion results. A potential solution lies in utilizing the smooth head observation during the recovery period after the pump is turned off, which yields more accurate travel times for inversion calculations. In this paper, the mathematical development suggests that the travel time of the recovery phase aligns with that of the pumping phase when pumping reaches a steady or quasi-steady state. Subsequently, by employing Monte-Carlo simulations, 1200 realizations of two-dimensional heterogeneous confined aquifer models were generated for simulating pumping tests with different pumping durations. The calculated head data were then utilized to compute the travel time derived from drawdown data (t) and recovery data (t′), respectively. Comparisons showed that t is equal to t′ when drawdown reaches a steady or quasi-steady state. Conversely, when the pump is turned off before reaching a quasi-steady state, t differs from t′. However, results also indicate the fact that a decent hydraulic travel time diagnosis can be obtained, especially for the cases when travel times are smaller than 15 s. Given the statistical results of Monte-Carlo simulations, as well as experience during pumping tests in the field with different scenarios, using the recovery data from 60 s of pumping duration, or extended pumping durations of 100 s or 200 s as a more conservative alternative, can replace the aquifer characterization based on drawdown data. The new inversion strategy not only has less data uncertainty and equivalent inversion accuracy, but also can greatly enhance the repeatability of field tests and reduce the environmental impact of long-term pumping tests.

Hydraulic tomography (HT) based on the successive linear estimator (SLE) offers the high-resolution characterization of aquifer heterogeneity but conventionally requires prolonged pumping to achieve steady-state conditions, limiting its applicability in contamination-sensitive or low-permeability settings. This study bridged theoretical and practical gaps (1) by identifying spatial periodicity (hole effect) as the mechanism underlying divergences in steady-state cross-correlation patterns between random finite element method (RFEM) and first-order analysis, modeled via an oscillatory covariance function, and (2) by validating a novel short-term sampling strategy for SLE-based HT using field experiments at the University of Göttingen test site. Utilizing early-time drawdown data, we reconstructed spatially congruent distributions of hydraulic conductivity, specific storage, and hydraulic diffusivity after rigorous wavelet denoising. The results demonstrate that the short-term sampling strategy achieves accuracy comparable to that of long-term sampling strategy in characterizing aquifer heterogeneity. Critically, by decoupling SLE from steady-state requirements, this approach minimizes groundwater disturbance and time costs, expanding HT’s feasibility to challenging environments.