Random Field Theory Research Articles

Characterisation of the spatial variability of underconsolidated Singapore Marine Clay using random field theory

ABSTRACT This paper characterised the spatial variability of Singapore Kallang Formation Marine Clays using piezocone penetration test (CPT) data from the Marina South area. Both vertical and horizontal scales of fluctuation in undrained shear strength for two distinct clay units, Upper Marine Clay (UMC) and Lower Marine Clay (LMC), are calibrated for autocorrelation and semi-variogram functions. The Marina South area was reclaimed from the sea using fills placed in three phases from 1970s to 1990s and remains underconsolidated up to date. This study identified variations in the degree of consolidation across the area, which has led to variations in the undrained shear strength in this area. However, the variations in the degree of consolidation were found to have no noticeable influence on the vertical and horizontal scales of fluctuation of either UMC or LMC unit. The vertical scales of fluctuation of UMC and LMC units are 0.57 ± 0.3 m and 0.48 ± 0.17 m , respectively, while the horizontal scales of fluctuations are 148 ± 26 m and 138 ± 28 m , respectively. The present study contributes to the database of the statistical and spatial variability of marine clays and can provide useful guidance for assessing reliability of excavations and foundations in Marina South as well as other areas with similar geological settings.

Novel Evaluation Method of 3D Joint Roughness Based on Random Field Theory

Novel Evaluation Method of 3D Joint Roughness Based on Random Field Theory

An One-step Triple Enhanced weakly supervised semantic segmentation using image-level labels.

Weakly supervised semantic segmentation, based on image-level labels, abandons the pixel-level labels relied upon by traditional semantic segmentation algorithms. It only utilizes images as supervision information, thereby reducing the time cost and human resources required for marking pixel data. The prevailing approach in weakly supervised segmentation involves two-step method, introducing an additional network and numerous parameters, thereby complicating the model structure. Furthermore, image-level labels typically furnishes only category information for the entire image, lacking specific location details and accurate target boundaries during model training. We propose an innovative One-Step Triple Enhanced weakly supervised semantic segmentation network(OSTE). OSTE streamlines the model structure, which can accomplish both pseudo-labels generation and semantic segmentation tasks in just one step. Furthermore, we augment the weakly supervised semantic segmentation network in three key aspects based on the class activation map construction method, thereby enhancing segmentation accuracy: Firstly, by integrating local information from the activation map with the image, we can enhance the network's localization and expansion capabilities to obtain more accurate and rich location information. Then, we refine the seed areas of the class activation map by exploiting the correlation between multi-level feature. Finally, we incorporate conditional random field theory to generate pseudo-labels with higher confidence and richer boundary information. In comparison to the prevailing two-step weakly supervised semantic segmentation schemes, the segmentation network proposed in this paper achieves a more competitive mean Intersection over Union (mIoU) score of 58.47% on Pascal VOC. Additionally, it enhances the mIoU score by at least 5.03% when compared to existing end-to-end schemes.

Efficient Random Field Generation With Rotational Anisotropy for Probabilistic SPH Analysis of Slope Failure

ABSTRACTDue to geological processes such as sedimentation, tectonic movement, and backfilling, natural soil often exhibits characteristics of rotated anisotropy. Recent studies have shown the significant impact of rotated anisotropy on slope stability. However, little research has explored how this rotated anisotropy affects the large deformations occurring after slope failure. Therefore, this study integrates rotated random field theory with smoothed particle hydrodynamics (SPH) to investigate its influence on post‐failure slope behavior. Focusing on a typical slope scenario, this research utilizes graphics processing unit (GPU)–accelerated covariance matrix decomposition (CMD) method to create rotated anisotropy random fields and applies the SPH framework for analysis. It examines the influence of rotated anisotropy angles and the cross‐correlation between cohesion and internal friction angle on landslides. The results indicate that the rotational anisotropy of the slope significantly influences post‐failure behavior. When the rotation angle is close to the slope surface, it tends to amplify both the magnitude and variability of slope failure. Furthermore, the study evaluates the efficiency of generating these random fields and emphasizes the substantial computational speed improvements achieved with GPU acceleration. These findings offer a robust approach for probabilistic analysis of slope large deformations considering rotated anisotropy. They provide a theoretical foundation for accurately assessing the risk of slope collapse, holding significant practical implications for geotechnical engineering.

Stability and failure probability analysis of super-large irregularly shaped deep excavation in coastal area considering spatial variability in soil properties

ABSTRACT The objective of this paper is to investigate the effects of spatial variability in coastal silty soil properties on the stability and failure probability of deep excavation. A super-large irregularly shaped deep excavation in the coastal area in Wenzhou, China, is considered. A numerical model is established based on the random field theory, finite difference method and Monte-Carlo simulation method. Focusing on the friction angle and cohesion, the effects of horizontal and vertical correlation distances and variation coefficients on excavation stability are systematically studied. Meanwhile, the reliability evaluation approach is also applied to systematically examine the impact of the correlation distance on the surface settlement and horizontal displacement of pile. The results show that the greater correlation distance leads to a larger dispersion degree of the ground settlement curve and the displacement curve of the diaphragm wall around. The influence of the horizontal correlation distance on land settlement is more significant. The horizontal and vertical displacements of the pile top are less affected by the correlation distance. Compared with the deterministic analysis, the random analysis results considering the soil spatial variability produce larger displacement.

Stochastic hazard assessment framework of landslide blocking river by depth-integrated continuum method and random field theory

AbstractLandslide-induced barrier dams pose a threat to the safety of humans, livestock and nearby infrastructures. The efficient assessment of landslide blocking river is crucial for disaster prevention and mitigation solutions. This study proposes a novel stochastic assessment framework to evaluate the landslide blocking river through the prediction of their deposition depths and considering the heterogeneity of shear strength parameters on the potential sliding surface. The depth-integrated continuum method (DICM) is used to simulate the landslide runout process. Using an enhanced Karhunen-Loève expansion (KLE) method, the spatial variations in soil's shear strength parameters are modeled by random fields to incorporate the effects of soil's spatial heterogeneity on the landslide deposition pattern. Subsequently, the multi-response surrogate model is constructed to relate the random field variables to the deposition depths based on extreme gradient boosting (XGBoost). To improve the performance of the surrogate model, principal component analysis (PCA) and sliced inverse regression (SIR) methods are employed for the dimension reduction of output and input variables, respectively. Furthermore, the algorithm for river blockage identification is developed to search for the deposition ridges. To demonstrate the capability of the stochastic assessment framework, an example of the first Baige landslide in Tibet, China is simulated, and the affected region and deposition depths of the landslide are predicted to calculate the probability of river damming. The presented methodology provides a practical means for improving the landslide blocking river prediction and new insights for early warning and risk mitigation.

Effects of Spatial Variation in Relative Density on Seismic Behavior of Saturated Sandy Ground

Proper consideration of variations in soil properties and their effects is necessary to enhance the seismic safety of structures. In this study, the effect of spatial variations in the cyclic resistance ratio on seismic ground behavior was investigated. Initially, dynamic centrifuge model tests were conducted on sandy ground featuring a 20% mixture of weak zones with low relative density and on homogeneous sandy ground with no mixture of weak zones. Subsequently, an effective stress analysis was performed by modeling the distribution of weak zones in the centrifuge model tests. Finally, after confirming the validity of the parameter settings, several analytical models with different weak-zone distributions were generated and numerically analyzed using random field theory. The results indicate that a local mixing of approximately 20% weak zones has only a limited effect on overall ground behavior. However, differences were observed in the rate of increase and dissipation of the excess pore water pressure ratio and in the residual horizontal displacement.

Predicting the elastic properties of Norway spruce by its morphology

Models for the elastic material properties of wood aim to predict the mechanical response of wooden structures to external loading. Traditionally, the variability of these properties in trees is described by a taxonomy of growth defects that is typically based on visual indicators in the material. This includes curvature, knots, and spiral grain models. Existing meso- and macro-scale models fail to describe the uncertainty connected to the local heterogeneity of the material. In this paper, we propose a novel meso-scale model that describes the natural variability of Norway spruce morphology and material properties based on random field theory. Our approach removes the need for a taxonomy of growth defects and enables uncertainty quantification of the stiffness and density in a straightforward fashion using simulations. This may enhance confidence for stiffness-graded applications, where the dynamic resonant behavior of wood structures is relevant and growth anomalies are present. Further, our stochastic models can generate images that realistically mimic wood patterns, which is relevant for applications like synthetic wood panels and flooring.

Computational modeling of near-fault earthquake-induced landslides considering stochastic ground motions and spatially varying soil

Landslides represent a large-deformation process influenced by various factors of uncertainty, such as types of ground motion (GM), randomness of GMs, and spatial variability of soils. The behavior of landslides is profoundly affected, making their assessment and measurement challenging. This paper proposes a computational approach for simulating the large-deformation process of landslides based on three-dimensional (3D) non-ordinary state-based peridynamics (NOSBPD). The analysis results of NOSBPD indicate that the mean runout distance triggered by pulse-like ground motions (PLGMs) is 16% greater than that induced by non-pulse ground motions (NPGMs), suggesting that PLGMs exhibit higher destructiveness. Besides, this paper establishes a runout distance assessment framework by considering the stochastic nature of PLGMs. This framework allows for the evaluation of the specific risk probability of landslides caused by stochastic PLGMs that match the target spectrum specified by codes. By introducing the theory of random fields and implementing a coupled procedure in peridynamics, we conducted a detailed analysis of the impact of spatial heterogeneity on the evolution process and consequences of landslides. Additionally, compared to two-dimensional (2D) analysis, the mean runout distance obtained from 3D analysis increased by 27.5%. This suggests that 2D analysis may underestimate the consequences of landslides. The findings of this study can serve as a scientific foundation for predicting the extent and scope of landslides triggered by near-fault earthquakes.

Identifying the centers of geographical public opinions in flood disasters based on improved conditional random field and focus theory

Location entities in social media data are helpful references for characterizing floods during the flood lifecycle; thus, accurately identifying location entities from social media data is a primary research topic. However, most researchers have used all locations identified from social media data to characterize floods, ignoring the characteristics of network public opinion, which represents a concentrated expression of online users’ opinions. Therefore, this study introduces the use of focus theory to define location entities. The location entities with focus attributes are defined as centers of geographical public opinion in flood disasters (CGeoPOFDs). In turn, these location entities can be used to characterize floods realistically. The model employs the front-back dynamic window and the semantic features of geographical location to improve the Conditional Random Field and applies correction functions to recall location labels and location entities. The study then applies the focus determination method to assign focus attributes to location entities and explores a method for identifying CGeoPOFDs. According to the results, the improved method and correction functions improve the recognition effect of location labels and location entities, confirming the success of using the focus determination method for focus semantic screening of all location entities. These results prove the authenticity of the CGeoPOFDs and the feasibility of the CGeoPOFDs identification method. This study opens up a new perspective on the use of social media data to characterize floods.

Evaluating the Characteristics of Spatial Variability of Soil in Vertical Direction Highly Heterogeneous Region Based on Cone Penetration Test

Abstract Key parameters describing the spatial variability of soil properties based on the random field theory are the scale of fluctuation (SOF) and coefficient of variation (COV). To characterize the spatial variability of soil properties, reducing the impact of these errors and uncertainties is necessary. To accomplish this, for the five main layers of soil, we collected 18 cone penetration test (CPT) data from a highly heterogeneous region in Lianyungang New Airport, Jiangsu Province, China, and used the control variable method to analyze the influence of the estimation method of tendency, its function type and outliers. The results show that, compared with the ordinary least square method (OLSM), the least absolute deviation method (LADM) can more truly reflect the trend component of CPT parameters in the vertical direction, and the influence of other factors on SOF and COV is also studied, such as outliers and estimation functions of trend components. On this basis, a reasonable calculation process of SOF and COV is summarized, which provides a reference for the calculation of SOF and COV in vertical direction in the future. By comparing the SOF calculated by different models, the results show that the squared exponential (SQX) model has the highest SOF in 68.3% of the evaluation, and the single exponential (SNX) model has the lowest SOF in 64.4% of the evaluation. Moreover, we compared the SOF and COV of cone tip resistance (qc) and sleeve friction (fs), which showed that SOF of qc and COV of qc is lower than that of fs in 54.4 and 73.3% of all evaluations, respectively.

A Method for Evaluating Systematic Risk in Dams with Random Field Theory

The parameters of gravity dams and foundation materials objectively exhibit spatial variability due to environmental and load influences, which significantly affect the safety status of dam structures. Therefore, a safety risk analysis method for a gravity dam–foundation system based on random field theory is proposed in this paper. Spatial variabilities in materials are particularly considered by using the finite element method. Then, composite response surface equations for the performance function (PF) of strength and stability failure are established, and then, the system failure risk is obtained using the Monte Carlo method. The proposed method solves the problem wherein the effect of spatial variability on failure risk cannot be reflected accurately by the performance function of multi-element sliding paths, and the difficulties in solving the failure risk of the series–parallel system due to multiple failure paths and their complex correlations. The application of a gravity dam shows that the developed method overcomes the disadvantages of the traditional method, such as the homogenization of the spatially random characteristics of parameters and the overestimation of failure risk in the system due to large variance estimation.

Uncertainty Analysis of Post-Failure Behavior in Landslides Based on SPH Method and Generalized Geotechnical Random Field Theory

In slope stability analysis, the inherent heterogeneity and spatial variability of soil significantly influence the aftermath of landslides, including critical aspects like runout distance, influence distance, and volume. This research integrates Smoothed Particle Hydrodynamics (SPH) with random field theory to precisely model the large deformation events in slopes with anisotropic shear parameters, while leveraging Graphics Processing Unit (GPU) parallel computing to expedite the generation of random field samples and SPH simulations. This approach meticulously examines how spatial heterogeneity of soil affects slope instability, simulating soil parameters across varied geological settings. It considers the fluctuation scale of anisotropy, the cross-correlation of cohesion and the angle of internal friction, along with their coefficient of variation (CV), to elucidate their impact on landslide magnitude and severity. This study furnishes a robust tool for a holistic assessment of slope impacts and landslide volumes. Additionally, by delineating the computational efficiency disparities between GPUs and Central processing units (CPUs), it underscores the pronounced efficiency benefits of GPU computing. The insights garnered offer fresh perspectives and methodologies in slope stability analysis and disaster risk evaluation, contributing to the finer prediction and management of this prevalent and grave geological hazard.

Dislocation flow turbulence simultaneously enhances strength and ductility

Multi-principal element alloys (MPEAs) exhibit outstanding strength attributed to the complex dislocation dynamics as compared to conventional alloys. Here, we develop an atomic-lattice-distortion-dependent discrete dislocation dynamics framework consisted of random field theory and phenomenological dislocation model to investigate the fundamental deformation mechanism underlying massive dislocation motions in body-centered cubic MPEA. Amazingly, the turbulence of dislocation speed is identified in light of strong heterogeneous lattice strain field caused by short-range ordering. Importantly, the vortex from dislocation flow turbulence not only acts as an effective source to initiate dislocation multiplication but also induces the strong local pinning trap to block dislocation movement, thus breaking the strength-ductility trade-off.

Unveiling deformation behavior and damage mechanism of irradiated high entropy alloys

The oxide dispersion strengthening (ODS) high entropy alloy (HEA) exhibits the high elevated temperature performance and radiation resistance due to severe atomic lattice distortion and oxide particles dispersed in matrix, which is expected to become the most promising structural material in the next generation of nuclear energy systems. However, microstructure and damage evolution of irradiated ODS HEA under loading remain elusive at submicron scale using the existing simulations owing to a lack of atomic-lattice-distortion information from a micromechanics description. Here, the random field theory informed discrete dislocation dynamics simulations based on the results of high-resolution transmission electron microscopy are developed to study the dislocation behavior and damage evolution in ODS HEA considering the influence of severe lattice distortion and nanoscale oxide particle. Noteworthy, the damage behavior shows an unusual trend of the decreasing-to-increasing transition with the continuous loading process. There are two main types of damage micromechanics generated in irradiated ODS HEA: the dislocation loop damage in which the damage is controlled by irradiation-induced dislocation loops and their evolution, the strain localization damage in which the damage comes from the dislocation multiplication in the local plastic region. The oxide particle hinders the dislocation movement in the main slip plane, and the lattice distortion induces the dislocation sliding to the secondary slip plane, which promotes the dislocation cross-slip and dislocation loop annihilation, and thus reduces the material damage in the elastic damage stage. These findings can deeply understand atomic-scale damage mechanism and guide the design of ODS HEA with high radiation resistance.

Altered Intrinsic Brain Spontaneous Activities in Children With Autism Spectrum Disorder Comorbid ADHD

Objective: The study involved 17 children with Autism Spectrum Disorder (ASD), 21 with ADHD, 30 with both (ASD + ADHD), and 28 typically developing children (TD). Methods: The amplitude of low-frequency fluctuations (ALFF) was measured as a regional brain function index. Intrinsic functional connectivity (iFC) was also analyzed using the region of interest (ROI) identified in ALFF analysis. Statistical analysis was done via one-way ANCOVA, Gaussian random field (GRF) theory, and post-hoc pair-wise comparisons. Results: The ASD + ADHD group showed increased ALFF in the left middle frontal gyrus (MFG.L) compared to the TD group. In terms of global brain function, the ASD group displayed underconnectivity in specific regions compared to the ASD + ADHD and TD groups. Conclusion: The findings contribute to understanding the neural mechanisms underlying ASD + ADHD.

Structural and functional changes following brain surgery in pediatric patients with intracranial space-occupying lesions.

We explored the structural and functional changes of the healthy hemisphere of the brain after surgery in children with intracranial space-occupying lesions. We enrolled 32 patients with unilateral intracranial space-occupying lesions for brain imaging and cognitive assessment. Voxel-based morphometry and surface-based morphometry analyses were used to investigate the structural images of the healthy hemisphere. Functional images were analyzed using regional homogeneity, amplitude of low-frequency fluctuations, and fractional-amplitude of low-frequency fluctuations. Voxel-based morphometry and surface-based morphometry analysis used the statistical model built into the CAT 12 toolbox. Paired t-tests were used for functional image and cognitive test scores. For structural image analysis, we used family-wise error correction of peak level (p < 0.05), and for functional image analysis, we use Gaussian random-field theory correction (voxel p < 0.001, cluster p < 0.05). We found an increase in gray matter volume in the healthy hemisphere within six months postoperatively, mainly in the frontal lobe. Regional homogeneity and fractional-amplitude of low-frequency fluctuations also showed greater functional activity in the frontal lobe. The results of cognitive tests showed that psychomotor speed and motor speed decreased significantly after surgery, and reasoning increased significantly after surgery. We concluded that in children with intracranial space-occupying lesions, the healthy hemisphere exhibits compensatory structural and functional effects within six months after surgery. This effect occurs mainly in the frontal lobe and is responsible for some higher cognitive compensation. This may provide some guidance for the rehabilitation of children after brain surgery.

Stability Analysis of Super-Large Special-Shaped Deep Excavation in Coastal Water-Rich Region Considering Spatial Variability of Ground Parameters

The excavation of a super-large foundation pit is a greatly risky project in coastal water-rich silt strata, and it is of great significance to establish a numerical model to analyze and predict the stability of the foundation pit retaining its structure for safe construction. Based on a geological investigation report and key node monitoring data, the model parameters have been modified. Subsequently, the random field theory and numerical analysis were employed to proceed with deterministic analysis and uncertainty analysis, respectively. Using the uniform distribution method, Gaussian distribution method and the covariance matrix method to generate a random field model, finite difference software was applied to analyze the impact of spatial variability of cohesion and the internal friction angle on structural deformation. The study shows that the overall distribution of axial force is small on both sides and large in the center, and the axial force is larger near the shaped region. Due to the principle of “lever”, there is a tendency for the horizontal displacement of surrounding piles to partially rebound from the pit when the bearing platform pit is excavated. The spatial variability of the internal friction angle and cohesion has an important influence on the numerical value of the enclosure structure and surface deformation, and the variation pattern is basically unchanged.

A Static Damage Constitutive Model of Concrete Based on Microscopic Damage Mechanism.

In this article, a microscopic constitutive model is established that includes friction, plastic, and spring elements and has clear physical meaning. The friction unit reflects the mutual friction between crack surfaces, the plastic unit reflects the development of concrete plasticity, and the fracture of the spring unit reflects the formation and expansion of interior cracks in concrete. In addition, the integration of the random field theory into this model uncovers the physical underpinnings of the relationship between concrete's nonlinearity and randomness. The multi-scale modeling of the concrete static damage constitutive model is then realized once the parameters of the random field are discovered using the macro test results. In order to apply the model's applicability in finite element programs, a subroutine was ultimately constructed. The experimental data and the anticipated values from the numerical simulation are in good agreement, supporting the model's realism.

Groundwater Responses of Foundation Subjected to Water Level Fluctuation of Reservoir Considering Variability of Layered Structure

The effect of the variability in a layered structure, characterized by the spatial variability of the saturated hydraulic conductivity, on the distribution of a pressure head p in a foundation subjected to water level fluctuation in a reservoir is investigated with the aid of the random field theory, Karhunen–Loève (K-L) expansion, first-order moment approach, and cross-correlation analysis. The results show that the variability in the foundation structure has significant impacts on the groundwater response to the reservoir’s water level fluctuations. Regions with relatively large uncertainties of the p and σp values in the foundation are those around the initial water level at the reservoir side, and those at the distal end away from the reservoir. In addition, there is a larger variance of Ks, denoted as σlnKs2, a larger correlation scale in the horizontal direction λh, a larger correlation scale in the vertical direction λv, and a larger one-way time consumption of fluctuations T to a larger uncertainty in p. Moreover, the four factors (σlnKs2, λh, λv, and T) all have positive correlations with σp. σlnKs2 has the largest impact on σp in the foundation, λv has the second largest impact, and λh has the smallest impact. A foundation with small Ks values around the initial water level at the reservoir side and large Ks values around the highest water level at the reservoir side may produce larger p values in the foundation. These results yield useful insight into the effect of the variability in a layered structure on the distribution of the pressure head in a foundation subjected to water level fluctuation in a reservoir.