A Physics-Informed Machine Learning Model for Displacement Forecasting of Deep-Seated Landslides

The variation of pore water pressure in earthen dams plays an important role in maintaining its stability. The pore water pressure within the dam are altered by the external loading conditions like rapid drawdown of reservoir water, earthquake loading and raise of water table caused by infiltration of rainfall. The seepage through an earthen dam involves saturated and unsaturated flows but to avoid complexity in solving the non-linear partial differential equations, the flow in unsaturated zone is neglected and seepage analysis is carried by constructing the flow net in which the pore water pressures beyond the free surface is taken as zero. In actual conditions negative pore water pressure develops beyond the free surface due to the capillarity which leads development to the matrix suction of the soil. In this paper a comparative study on distribution of pore pressure in a zoned earthen dam under steady state and transient conditions had been carried out considering unsaturated-saturated seepage theory. To solve the non-linear partial differential equations, finite element method has been adopted in the present study. The earthen dam has been modeled in different stages. At each stage a new parameter was added and parametric analysis was carried out. The results indicate that negative pore water pressure developed at the downstream side and the pore pressures at the mid-levels of the core are high. This specifies that, soils with low permeability have higher pore pressure. The pore pressures appeared to be higher in upstream side during rapid drawdown compared to steady state.

Rainfall-induced landslides are a significant hazard in many areas of loess-covered terrain in Northwest China. To investigate the response of a loess landslide to rainfall, a series of artificial rainfall experiments were conducted on a natural loess slope, located in the Bailong River Basin, in southern Gansu Province. The slope was instrumented to measure surface runoff, pore water pressure, soil water content, earth pressure, displacement, and rainfall. The hydrological response was also characterized by time-lapse electrical resistivity tomography. The results show that most of the rainfall infiltrated into the loess landslide, and that the pore water pressure and water content responded rapidly to simulated rainfall events. This indicates that rainfall infiltration on the loess landslide was significantly affected by preferential flow through fissures and macropores. Different patterns of pore water pressure and water content variations were determined by the antecedent soil moisture conditions, and by the balance between water recharge and drainage in the corresponding sections. We observed three stages of changing pore water pressure and displacement within the loess landslide during the artificial rainfall events: Increases in pore water pressure initiated movement on the slope, acceleration in movement resulting in a rapid decrease in pore water pressure, and attainment of a steady state. We infer that a negative pore water pressure feedback process may have occurred in response to shear-induced dilation of material as the slope movement accelerated. The process of shear dilatant strengthening may explain the phenomenon of semi-continuous movement of the loess landslide. Shear dilatant strengthening, caused by intermittent or continuous rainfall over long periods, can occur without triggering rapid slope failure.

Loess landslides are one of the most important natural hazards among various landslide types in China, and rainfall is the main factor triggering loess slope instability. To gain deeper insights into the processes behind slope failure triggered by precipitation, this study conducted an indoor slope rainfall modelling test based on the case of the Shixiakou landslide in Jinzhou, Lanzhou. The test employed a custom-built rainfall simulation device, precisely controlling rainfall intensity and duration to mimic natural rainfall conditions. Soil moisture sensors, pore-water pressure transducers, and strain gauges were strategically installed within the loess slope model to monitor soil moisture dynamics, pore-water pressure variations, and lateral stress distribution in real-time. This investigation examined the progressive failure mechanism of loess slopes under rainfall infiltration through integrated monitoring. The experimental results demonstrate that sustained precipitation triggers a sequential failure process characterized by four distinct phases: initial surface scouring, subsequent basal slope instability, progressive mid-slope shear failure, and ultimate crown section collapse, and finally traction failure mode. It is worth noting that cracks play a crucial role in slope failure by creating preferential channels for water infiltration and subsequent failure development.

This study used an inventory of debris flow triggered by a storm event in Colorado Front Range as an example to compare the capability of data-driven and physics-based approaches for regional-scale debris flow susceptibility mapping (LSM). Nine debris flow contributing factors were collected for the present study based on the availability of geophysical data in the study area. These contributing factors represent hillslope geometries, surface hydrology, and soil conditions. For the physics-based approach, the infinite slope model was used to directly determine the debris flow susceptibility for the study area by calculating the factor of safety (FS) based on parameters derived from geophysical data. For the data-driven approach, an artificial neural network (ANN) was developed to predict debris flow susceptibility for the study area by learning relationships from the contributing factors using the debris flow inventory. The results showed that both physics-based and data-driven models predicted debris flow susceptibility in the study area with relatively high accuracy; the data-driven approach outperformed the physics-based approach as it could extract complex features which the physics-based approach did not consider.

In this study, a laboratory model test on utilization of recy cled aggregates and crushed stone as vertical drains to use alternative material of sand in soft ground is performed. The v ertical and horizontal coefficient of permeability of the recyc led aggregates and crushed stone showed largely 1.2～4.0 times and 3 .0～3.3 times greater than sand, respectively. Therefore, it showed enough to be an alternative material to the sand which had been being used as the vertical and horizontal drainage material before. The variations of pore water pressure with time showed constantly regardless of the load in all vertical drainage materials. When water level drops suddenly, the pore w ater pressure of the recycled aggregate and crushed aggregate is reduced to nearly zero. Therefore, it was applicab le to the field because discharge capacity was similarity to th at of sand. The settlement in crushed aggregates and recycled aggregate decreases gradually with the load increase. When water level drops suddenly, earth pressure in all drains materials was evaluated the equivalent drainage capacity similarity to sand because it show approaching the nearly zero. Key words: Recycled aggregates, crushed stone, drain material, pore water pressure, settlement, earth pressure

Experimental study of one-dimensional nonlinear consolidation of an aquitard under multistage loading

Stresses and pore water pressure induced by machine foundation on saturated sand

The utilization of data-driven models in hydrology has witnessed a significant increase in recent years. The open-source philosophy underpinning much of the code developed and research being conducted has facilitated widespread access to the the hydrological community to sophisticated machine learning models and technology (Reichstein 2019). These data driven approaches to hydrological modelling has witnessed growing interest after multiple studies has shown how machine-learning models were able to outperform nationwide traditional physics-based hydrological models (Kratzerts et al. 2019). The latter often demands substantial man-hours for development, calibration and fine-tuning to accurately represent relevant hydrological processes. In this national-scale explorative study we undertake an in-depth examination of Danish catchment hydrology. Our objective is to understand what processes and dynamics are well captured by a purely data driven model without physical constraints, namely the Entity-Aware Long Short-Term Model (EA-LSTM). The model code was developed by Kratzerts et al. (2019) and the analysis build on top of a newly published national CAMELS data set covering 301 catchments in Denmark (Koch and Schneider, 2022), with an average resolution of 130 km2. Denmark, spanning an area of around 43 000 km2, demonstrates a relatively high data coverage. Presently more than 400 stations record water level measurements in the Danish stream network, while a network of 243 stations have collected meteorological data since 2011. These datasets maintained by the Danish Environmental Protection Agency and the Danish Meteorological Institute, respectively, and are publicly available. Despite Denmark’s data abundance, Koch and Schneider (2022) demonstrated that the data-driven EA-LSTM model, trained with the CAMELS dataset for Denmark (from now on referred to as the DK-LSTM) were not able to outperform the traditional physics-based hydrological model, against which it was benchmarked. Consequently, performance of the DK-LSTM model could be increased by pre-training it with simulations from a national physics-based model indicating that dominating hydrological processes are not described by the readily available input data in the CAMELS dataset. This study conducts a comprehensive analysis of Danish catchment hydrology aiming to explore three aspects: 1) the common characteristics of the catchments where the DK-LSTM performs well or encounters challenges, 2) the identification of hydrological characteristics, that exhibit improvement when informing the data-driven model with physics-based model simulations, and 3) an exploration of whether the aforementioned findings can guide us in determining necessary physical constraints and/or input variables that explains the hydrological processes for the data-driven model approach at a national scale, using the example of DK-LSTM.   Koch, J., and Schneider, R. Long short-term memory networks enhance rainfall-runoff modelling at the national scale of Denmark. GEUS Bulletin, 49. https://doi.org/10.34194/geusb.v49.8292, 2022. Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., and Nearing, G.: Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets, Hydrol. Earth Syst. Sci., 23, 5089-5110, https://doi.org/10.5194/hess-23-5089-2019, 2019. Reichstein, M., Camps-Valls, G., Stevens, B. et al. Deep learning and process understanding for data-driven Earth system science. Nature 566, 195–204. https://doi.org/10.1038/s41586-019-0912-1, 2019.

The classical step-by-step integration method is commonly used for solving structural dynamic responses, but its performance is highly sensitive to the choice of time step. A large time step can significantly reduce accuracy and stability, while a very small time step greatly diminishes computational efficiency. Data-driven modeling and analysis methods are particularly favored for their potential to replace traditional structural analysis methods. However, traditional data-driven machine learning approaches require substantial amounts of training data to predict structural dynamic responses. Moreover, these methods often function as black boxes, lacking physical interpretability, and acquiring the necessary data can be challenging in practice. To address these limitations, this paper employs a physics-informed neural network (PINN) method for structural dynamic response analysis. The PINN approach incorporates the governing equations of structural dynamics into the neural network’s loss function as physical constraints, endowing the model with physical interpretability. The feasibility and effectiveness of this method are demonstrated through case studies on structural dynamic responses under different excitation scenarios. Numerical results show that the PINN method can accurately analyze structural dynamic responses without relying on system response data, a key advantage over traditional data-driven models. Moreover, unlike the classical step-by-step integration method, the PINN approach operates as a spatial domain optimization process and is independent of time step. Given the critical role of hyperparameters in the performance of the PINN model, this paper systematically investigates the influence of various hyperparameter settings on accuracy and efficiency, uncovering patterns of their impact on structural response analysis. Replication code for this paper will be available on GitHub:https://github.com/duke-iem/AIStructDynSolve.

In this study, the full-scale laboratory model test on utilization of recycled aggregates and crushed stone as vertical drains to use an alternative material of sand in soft ground is performed. The settlement and pore water pressure were measured to evaluate the discharge capacity and filed application, and the results were compared and analyzed through the finite element method. The measured and estimated settlement in all vertical drain materials decreases gradually with the load increase. The measured settlement 6.55~8.63 mm, and the estimated by the Hyperbolic model was 7.45~7.92 mm. So the model used for the analysis can be applied to the settlement estimation of the actual field. The variations of pore water pressure with time showed constantly regardless of the load in all vertical drainage materials. The pore water pressure was similarity to that of sand after rapid drawdown. Therefore, it was applicable to the field because discharge capacity was enough to be an alternative material to the sand which had been being used as the vertical drains.

Excavation-induced unloading effects and dewatering-induced groundwater seepage inevitably result in basal soil reverse consolidation in deep excavation. However, this reverse consolidation process is rarely considered because most previous analytical methods were developed based on total stress analyses. This study proposes a one-dimensional reverse consolidation model for basal soil of deep excavation. Based on the consolidation theory proposed by Terzaghi, governing equations of soil reverse consolidation caused by excavation and dewatering were separately established. The continuous drainage boundary was introduced to describe the construction processes. The reverse consolidation responses of basal soil were obtained by superimposing analytical solutions of the excess pore-water pressures that resulted from excavation and dewatering. The proposed model was verified by existing solutions and a well-documented excavation case history. Moreover, the reverse consolidation characteristics of basal soil were investigated by parametric analyses. Results indicate that the excavation-induced variations in pore-water pressure decreased with increasing excavation depth. The final pore-water pressure and effective stress were predominantly affected by excavation duration rather than interval distribution. In addition, a smaller coefficient of consolidation led to lower pore-water pressure and greater effective stress at a given excavation depth.

Discretization-based methods like the finite element method have proven to be effective for solving the Helmholtz equation in computational acoustics. However, it is very challenging to incorporate measured data into the model or infer model input parameters based on observed response data. Machine learning approaches have shown promising potential in data-driven modeling. In practical applications, purely supervised approaches suffer from poor generalization and physical interpretability. Physics-informed neural networks (PINNs) incorporate prior knowledge of the underlying partial differential equation by including the residual into the loss function of an artificial neural network. Training the neural network minimizes the residual of both the differential equation and the boundary conditions and learns a solution that satisfies the corresponding boundary value problem. In this contribution, PINNs are applied to solve the Helmholtz equation within a two-dimensional acoustic duct and mixed boundary conditions are considered. The results show that PINNs are able to solve the Helmholtz equation very accurately and provide a promising data-driven method for physics-based surrogate modeling.

Triggered seismicity arising from dynamic stresses is often explained by the Mohr‐Coulomb failure criterion, where elevated pore pressures reduce the effective strength of faults in fluid‐saturated rock. The seismic response of a fluid‐rock system naturally depends on its hydromechanical properties, but accurately assessing how pore fluid pressure responds to applied stress over large scales in situ remains a challenging task; hence, spatial variations in response are not well understood, especially around active faults. Here I analyze previously unutilized records of dynamic strain and pore pressure from regional and teleseismic earthquakes at Plate Boundary Observatory (PBO) stations from 2006 to 2012 to investigate variations in response along the Pacific/North American tectonic plate boundary. I find robust scaling response coefficients between excess pore pressure and dynamic strain at each station that are spatially correlated: around the San Andreas and San Jacinto fault systems, the response is lowest in regions of the crust undergoing the highest rates of secular shear strain. PBO stations in the Parkfield instrument cluster are at comparable distances to the San Andreas Fault (SAF), and spatial variations there follow patterns in dextral creep rates along the fault, with the highest response in the actively creeping section, which is consistent with a narrowing zone of strain accumulation seen in geodetic velocity profiles. At stations in the San Juan Bautista (SJB) and Anza instrument clusters, the response depends nonlinearly on the inverse fault‐perpendicular distance, with the response decreasing toward the fault; the SJB cluster is at the northern transition from creeping‐to‐locked behavior along the SAF, where creep rates are at moderate to low levels, and the Anza cluster is around the San Jacinto Fault, where to date there have been no statistically significant creep rates observed at the surface. These results suggest that the strength of the pore pressure response in fluid‐saturated rock near active faults is controlled by shear strain accumulation associated with tectonic loading, which implies a strong feedback between fault strength and permeability: dynamic triggering susceptibilities may vary in space and also in time.

In order to research on slope seepage field and slop stability under rainfall infiltration, this paper combines finite element with limit equilibrium theory to study. The results show that under rainfall, pore water pressure of the slope crest and slope toe in slope wash is greatly influenced by rainfall; Change in the volume moisture content is more sensitive than pore water pressure, volumetric moisture content of each location is increasing quickly at the initial stage of rain, volumetric moisture content in the lower locations is the first to reach saturated due to the continued supply and gravity of the rain; The slope stability reduces with rainfall infiltration, the greater the rainfall intensity, the more obvious decline the slope safety factor.

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.