3D Stability Analysis Research Articles

Physics-guided neural network-based framework for 3D modeling of slope stability

Physics-informed neural networks (PINN) have gradually attracted attention in the field of geotechnical engineering. This paper proposes a novel PINN-based framework for the three-dimensional (3D) stability analysis of soil slopes. Based on the fundamental theorem of plasticity and limit analysis, the partial differential equations (PDE) with regard to slope collapse are derived and integrated into the physics-guided loss function. A kinematically admissible failure mechanism that rigorously satisfies the Mohr-Coulomb associated flow rule is obtained by minimizing the loss function, thereby circumventing complex mathematical calculations. The discrete points generated by PINN are selected and refined through a series of procedures to represent the failure block of slopes using a two-dimensional matrix. The entire training process of the PINN-based framework is conducted without the need for any labeled data. The resulting discretized failure mechanism is meshfree and capable of accommodating spatially discrete data. A validation exercise is performed to verify the proposed framework by comparing it with the classical 3D rotational failure mechanism. To further consider the impact of external excitation on slope stability, a hybrid PINN framework is developed to assess the stability of slopes subjected to complex external environments. In addition to the PINN to generate a failure mechanism, a parallel PINN is employed to acquire the corresponding spatially discrete data of specified external excitations. The hybrid PINN framework for seismic stability assessment of slopes is demonstrated by way of example, indicating favorable feasibility and applicability of the developed approach. The proposed PINN-based framework provides innovative and promising avenues for 3D slope stability analysis.

3D Stability Analysis of Soil–Rock Tunnel Faces: Pore Water Pressure and Partial Failure Perspectives

3D Stability Analysis of Soil–Rock Tunnel Faces: Pore Water Pressure and Partial Failure Perspectives

Local gravitational instability of two-component thick discs in three dimensions

Aims. The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study the local gravitational instability of two-component thick discs in three dimensions. Methods. We use as a starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness that takes the form Q3D < 1, where Q3D is a 3D version of the classical 2D Toomre Q parameter for razor-thin discs. Here, we extend the 3D stability analysis to two-component discs, considering first the influence on Q3D of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations. Results. We find that Q3D < 1, where Q3D can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have Q3D > 1.

3D stability analysis of submarine slopes: a probabilistic approach incorporating strain-softening behaviour

3D stability analysis of submarine slopes: a probabilistic approach incorporating strain-softening behaviour

Damage assessment of Siverek Castle during the Kahramanmaraş Earthquakes (Mw 7.7 and Mw 7.6) on 06 February 2023: Remediation and strengthening proposals

On February 6, 2023, two significant earthquakes with magnitudes (Mw) of 7.7 and 7.6 struck Turkey, occurring nine hours apart. In addition to the tragic loss of over 50,000 lives in the earthquakes centered in Kahramanmaraş, hundreds of thousands of engineering structures, such as residences, schools, hospitals, historical landmarks, highways, and more, were severely damaged. This study assesses the damages and risk scenario following the Kahramanmaraş earthquakes concerning Siverek Castle. In addition, remediation and strengthening proposals, required to eliminate the damage and the possible risk, have been developed. The initial stage involved observational damage assessments on the castle and surrounding slopes as part of field studies, identifying five different types of damage and potential risks. Subsequently, a precise 3D digital model of the damaged castle and its slopes was generated using the digital photogrammetry method. Additionally, geological and geophysical studies were conducted in the field to determine the characteristics of the mound structure, historical castle walls, soil and rock on the slope. Non-destructive, geophysical methods consisting Vertical Electrical Sounding (VES), Seismic Refraction Method (SRM) and Multichannel Analysis of Surface Waves (MASW) measurements were specifically employed in the area with historical remnants. To verify the obtained data, five boreholes were drilled in the lower parts of the slope, and experimental studies were conducted to determine the soil and rock material properties of the slope. In the numerical studies, a total of 54 2D stability analyses were performed under static, long-term static, and dynamic conditions. Additionally, 1000 different probabilistic rockfall analyses were conducted, both in 2D and 3D, to calculate the run-out distance, bounce height, velocity, and kinetic energies of the blocks that fell or were about to fall during the earthquake. In the final stage of the study, remediation and strengthening recommendations were prepared for the strengthening of the fortification walls and slopes where failures occurred, and stability analyses were conducted. Consequently, a design proposal recommending five distinct approaches to remediate and strengthen the castle and slopes impacted by the Kahramanmaraş earthquakes was endorsed by the relevant authorities, and construction has commenced. When the remediation and strengthening works are completed, the security of the cultural heritage will be ensured, and it is planned to be opened to visitors.

Three‐dimensional stability analysis for a deep‐buried tunnel roof considering soil stratum strength nonlinearity

AbstractA three‐dimensional (3D) collapse mechanism was employed in this work to investigate the roof stability of deep‐buried cylindrical tunnels in soil considering strength nonlinearity. Based on the kinematic approach of limit analysis, three tunnel roof stability measures, namely, the stability number, the required support pressure, and the factor of safety solutions were derived to provide quantitative indicators for evaluating tunnel roof stability. Optimal upper bound solutions for these measures were obtained through optimization. Subsequently, the effects of soil strength nonlinearity and 3D geometry characteristics on roof stability and the profiles of collapsing blocks were investigated: The increase in the nonlinear coefficient m and the tensile strength σt, as well as the decrease in the initial cohesion c0, will lead to a deterioration in the stability of the tunnel roof, and also result in a larger range of collapse blocks of the tunnel roof. A 3D stability analysis of the tunnel roof can provide more reasonable stability estimates than a 2D stability analysis. When the length‐to‐radius ratio L/R → ∞, the 2D solution results.

A 2D stability analysis of the rock surrounding underground liquified natural gas storage cavern based on COMSOL Multiphysics

Underground liquified natural gas (LNG) storage is essential in guaranteeing national energy strategic reserves, and its construction is being accelerated. The stability of surrounding rock of underground LNG storage caverns under stress-low temperature coupling effect is the key factor determining the feasibility of LNG storage. First, a mathematical model used for controlling the stress-low temperature coupling and the processes of rock damage evolution is given, followed by a 2-D numerical execution process of the mathematical model mentioned above described based on Comsol Multiphysics and Matlab code. Finally, a series of 2-D simulations are performed to study the influence of LNG storage cavern layout, burial depth, temperature and internal pressure on the stability of surrounding rocks of these underground storage caverns. The results indicate that all the factors mentioned above affect the evolution of deformation and plastic zone of surrounding rocks. The research results contribute to the engineering design of underground LNG storage caverns.

Simulation analysis of 3D stability of a landslide with a locking segment: a case study of the Tizicao landslide in Maoxian County, southwest China

Abstract. Rock bridges, also known as locking masses in landslides, affect the three-dimensional (3D) stability and deformation patterns of landslides. However, it is always difficult to simulate rock bridges with continuous grid models in 3D landslides due to their discontinuous deformations. Tizicao landslide, located in Maoxian County, southwest China, is a typical landslide with a super-large rock mass volume of about 1388.2 × 104 m3 and a locking segment. To explore a better rock bridge model used to simulate 3D stability and deformations of the Tizicao landslide, this study introduced three rock bridge models into the FLAC3D program, including the intact rock mass model (IRMM), the Jennings model (JM), and the contact surface model with high strength parameters (CSM-HSP). The CSM-HSP model was eventually used in the FLAC3D program to obtain the 3D deformation characteristics of the landslide. In addition, the two-dimensional (2D) stability of the Tizicao landslide was analyzed using the GeoStudio program. The simulation results indicate that the Tizicao landslide is generally stable under current conditions owing to the existence of the locking segment in its southern front. This inference is consistent with the field deformation and monitoring data. It was found that the general stability and local deformations of the landslide are influenced by the locking segment according to the comparison between the 2D and 3D stability. There was a linear relationship between the locking ratio and the factor of safety (Fos), which applied to the 2D stability analysis of the landslides with a locking segment each, while there existed an approximate quadratic parabola suitable for the 3D stability of the landslides. Finally, this study analyzed the laws of the 3D Fos varying with the locking ratio and strength parameters of the locking masses and the sliding surface. Furthermore, it explored the advantages and disadvantages of the three rock bridge models in the simulation of the 3D stability of landslides with a locking segment.

Three-dimensional stability analysis of two-layer slope based on GIS under rainfall conditions

ABSTRACT Geographical Information System (GIS), as a computer-based tool, allows easy data processing, and complex geospatial data management and analysis, making it a suitable environment for 3D slope stability analysis. The study proposed an integral scheme for 3D stability analysis of a two-layer slope under rainfall conditions based on GIS. To construct the 3D model of the slope and the sliding surface in GIS, a method was proposed in which a grid is divided into four sections to improve the accuracy of calculation, and the extension of the Hovland model and the Janbu model in unsaturated soil was discussed. The transformation equations between the global coordinates and the ellipsoid local coordinates were derived to locate the critical sliding surface, and how to apply constraints of parameters to improve search efficiency was put forward. An infiltration model for a two-layer slope was built so that the changes in water content in slope at the both stages of rainwater infiltration and redistribution can be determined, and the model was integrated into the GIS-based scheme to assess the impact of rainfall on slope stability. Finally, two case studies were implemented to demonstrate the validity and correctness of the proposed scheme.

Effect of Rock Mass Disturbance on Stability of 3D Hoek–Brown Slope and Charts

The present study performs a stability analysis of a three-dimensional (3D) rock slope in disturbed rock masses following the Generalized Hoek–Brown (GHB) failure criterion. The factor of safety (FoS) of the slope is derived and the optimal solution is captured combining the limit analysis method and the strength reduction technique. It is indicated by the parametric analysis that the 3D geometric characteristics have a significant impact on slope stability such that FoS decreases sharply with the increase in the width-to-height ratio B/H within 0<B/H≤2.0 and thereafter reaches a constant value asymptotically. The FoS decreases more than 60% linearly when the disturbance factor D increases from 0 to 1.0. Stability charts and slope angle weight factor fβ_3D for 3D slopes are proposed to provide a convenient and straightforward approach to obtain the FoS solutions of 3D slopes. A case study was carried out to apply the stability charts on practical engineering cases, which showed that slope stability under two-dimensional (2D) plane strain will lead to conservative results, and a 3D stability analysis of slope is more appropriate, especially for a slope with a limited width.

Case study: 3D mobilized strength of compacted fill

Water infiltration can cause softening of compacted structural fill and a reduction of the shear strength from the peak compacted strength to the fully softened strength (FSS) with an accompanying reduction in drained factor of safety (FoS). This study presents two-dimensional (2D) and 3D stability analyses of a compacted fill slope failure that occurred 6 years after construction due to water leaking from a connection between the main and lateral water pipes in the water supply system. The compacted fill material primarily consists of high plasticity fine-grained soil. The 3D FoS at the end of construction is 2.44 using the peak compacted strength envelope. However, the 3D FoS is close to unity (1.0) when the FSS is assigned to the compacted fill material with the appropriate piezometric surface, which means the 2 H:1 V compacted fill slope softened to the FSS within 6 years. This is an interesting FSS case because the failure surface is 4 m deep and semi-circular, which differs from infiltration cases that exhibit a shallower and more planar surface.

Physical Model Tests of Concrete Buttress Dams with Failure Imposed by Hydrostatic Water Pressure

Although the failure of a concrete dam is a complex and highly dynamic process, the current safety assessments of concrete gravity and buttress dams rely on a simplified 2D stability analysis, which neglects the load redistribution due to 3D monolith interactions and the valley shape. In addition, the estimation of breach parameters in concrete dams is based on assumptions rather than analyses, and better prediction methods are needed. Model tests have been conducted to increase the understanding of the failure behavior of concrete dams. A scale model buttress dam, with a scale of 1:15, consisting of 5 monoliths that were 1.2 m in height and 4 m in width, was constructed and loaded to failure using water pressure. The model dam had detachable abutment supports and shear keys to permit variations in the 3D behavior. The results showed that the shear transfer was large between the monoliths and that the failure of a single dam monolith is unlikely. A greater lateral restraint gives not only a higher failure load but also a better indication of impending failure. These findings suggest that the entire dam, including its boundary conditions, should be considered during a stability assessment. The results also suggest that the common assumption in dam safety codes that a single monolith fails during flooding analysis is not conservative. The dataset obtained provides a foundation for the future development of dam-monitoring alarm limits and for predictive models of dam-breaching processes.

First order reliability-based design optimization of 3D pile-reinforced slopes with Pareto optimality

As verified structures for landslide mitigation, stabilizing piles are often adopted to treat local failure zones of width-limited soil slopes. To achieve a balance between slope safety and construction cost, an optimized piling scheme for treating width-limited soil slopes should be obtained through three-dimension (3D) stability analysis. In this regard, this paper presents a novel calculation framework for the multi-objective optimization (MOO) design of stabilizing piles. It is based on the first-order reliability method (FORM) and considers a 3D width-limited slope failure with geological uncertainties. The study first develops a deterministic 3D stability model of pile-reinforced slopes using limit analysis. Accounting for soil shear strength uncertainties, reliability analyses of 3D reinforced slopes are conducted based on the prescribed pile-reinforcement patterns. Then, a multi-objective probabilistic design procedure combining the Pareto front and reliability analysis results is proposed. The effectiveness and significance of the proposed MOO design framework are demonstrated through two illustrative examples: one involves designing stabilizing piles in a homogenous slope, and the other involves designing for an inhomogeneous earth slope with depth-dependent soil cohesion. To gain better understanding of the probabilistic impact of uncertain pile design parameters on reinforced slope stability, comprehensive parametric studies are conducted.

3D limit analysis of rock slopes based on equivalent linear failure criterion with tension cut-off

Hoek-Brown (HB) failure criterion is widely used to predict the strength of intact or heavily jointed rock mass. For stability analysis of rock slopes governed by the HB failure criterion, the equivalent linearity to Mohr-Coulomb (MC) criterion is often adopted, leading to the well-known equivalent Mohr-Coulomb method (EMCM). Existing studies on EMCM analysis mainly consider the shear strength of rock material, while consideration of the tensile strength is rare. This contradicts the fact that the underlying tensile strength of rock mass has considerable impact on the rock slope stability in real world. In this regard, this paper proposes a limit analysis-based approach that can account for tension in the three-dimensional (3D) stability analysis of HB rock slope. This approach is established on the equivalent linearity of the HB criterion with consideration of tensile strength, known as the equivalent tension cut-off MC method (ETMCM), and using a horn-like 3D mechanism of limit analysis. The safety factor solutions given by the proposed approach are validated by previous studies and numerical results. Parametric studies are conducted to investigate the effect of rock tensile strength on slope stability. Results show that the consideration of tension leads to a more conservative safety factor and a sharper curvature of the failure surface, and these impacts tend to be more obvious with the increases in slope inclination and slope width. Finally, the stability of the HB rock slope under seepage conditions is studied using the proposed approach. The results indicate that the effect of tensile strength is highly remarkable in seepage circumstances.

Three-Dimensional Stability Analysis of Ridge Slope Using Strength Reduction Method Based on Unified Strength Criterion

Ridge slopes often occur in highway or railway engineering. The initial stress distribution of a ridge slope is important for the original slope and an excavation slope. In this paper, a wire-frame model of ridge slope was established. Numerical simulations on the 3D stability analysis were performed using the strength reduction method based on unified strength theory. The influences of ridgeline dip angle α, flank slope angle β, and slope height H on the deformation and failure mode of ridgeline slopes were analyzed. When α was small, cracking failure easily occurred at the front edge of the ridge slope and the area near the ridge line. When α was large, shear failure was prone to occur at the trailing edge of the ridge slope. Under the same reduction coefficient, the larger the flank slope angle β, the larger the slope displacement of the ridge. The plastic zone gradually concentrated near the ridge. When H was small, the displacement mainly occurred at the trailing edge of the slope, and the slopes were generally prone to cracking damage at the trailing edge. The front edge of the slope experienced a large displacement when the height of the ridge slope increased. The bottom of the flank slope was also displaced, and a plastic zone was observed at the foot of the slope. When the excavation slope ratio of the ridge slope was small, the plastic zone was mainly located on the side slope. When the excavation rate increased, the plastic zone appeared on the excavation slope surface, and its stability decreased significantly.

Stability analysis of a slope and runout analysis movement of the mobilized-mass volume

This research aims to present a deterministic and probabilistic analysis of the stability in 2D/3D of a road slope, located in the state of São Paulo, Brazil, in the Serra Pelada region, incorporating scenarios with and without surface suction and water level, and predict the movement of the mobilized-mass volume. The results of the stability analysis showed the variability of the safety factor, the probability of failure, and the mobilized-mass volume, in the twenty-six simulated scenarios. The results of the runout analysis of the mobilized-mass volume indicated that any possible landslide would interdict, at least, two of the three lanes of traffic, equivalent to 59.7% of the lanes. Therefore, it can be concluded that a 2D and 3D stability analysis combined with the material point method to predict the post-failure soil displacement provides a better understanding of all processes involved in a landslide, which helps to establish more adequate and effective mitigation and remedial measures for each situation. Finally, in conclusion, the studied slope, with a maximum failure probability of 1.24%, is safe in terms of its overall stability for all twenty-six simulated scenarios.

Global linear stability analysis of the flow inside a conical draft tube

The paper presents the numerical simulations of the flow inside the draft tube of Francis-99 turbine at the part load (PL) operating condition. The rotating vortex rope (RVR) is a phenomenon that occurs during the PL operating regime inside the draft tube of hydraulic turbines. To reduce the computational cost, the numerical simulations are carried out in two steps. Firstly, steady state numerical simulations are performed in a reduced geometry of the runner which is made of a runner passage and part of the draft tube. The velocity profiles from the steady state simulation are used as a boundary condition for unsteady numerical simulation on the inlet of the full draft tube geometry. The velocities from the numerical simulations are time-averaged over a period of 5 RVR rotations and validated with the experimental velocities averaged over the same period. Further, a two-dimensional (2D) linear global stability analysis is performed on a plane extracted from the cone of the draft tube using the time-averaged flow. The frequency of three-dimensional (3D) flow simulation and of the 2D stability analysis are found to be in good agreement with the experimental frequency.

Time History Method of Three-Dimensional Dynamic Stability Analysis for High Earth-Rockfill Dam and Its Application

Accurately grasping the stability characteristics of high earth-rockfill dam slopes is the key to the seismic safety evaluation of dams. In this research, the development and application of the common methods for slope stability analysis are reviewed firstly. Then, a three-dimensional dynamic time history stability analysis method is presented, and corresponding software is developed based on the sliding surface finite element stress method combined with the three-dimensional finite element dynamic response. This method makes the three-dimensional dynamic stability analysis efficient, and the effectiveness of this software is verified. Finally, the two-dimensional (2D) and three-dimensional (3D) dynamic stability analyses of a high concrete face dam are carried out, and the stability of the dam’s downstream slope under seismic load is studied. The results indicate that there are many differences between the results of the traditional 2D and 3D stability analyses. The time history of the safety factor, local safety behavior, overall shape and spatial position of the potential sliding body, and even the sliding process of failure can be captured with 3D stability analysis.

3D stability analysis method for toppling failure on rock slopes

In this paper, an optimized solution method is proposed for the 3D stability analysis of rock slopes subject to toppling failure, based on their geometric and mechanical properties. It was verified by a 3D block system that focused on the geometric properties of toppling slopes, considering the force and its action point on the interface of the block system as unknown variables, as well as introducing the definition of a safety factor considering both tension and shear strength reduction. The proposed method implied setting constraints, such as the balance equation corresponding to block force and moment, as well as non-violation of the yield criterion, considering the minimum value of the safety factor as the objective function. It was applied to the analysis of two typical 3D models simulating toppling failure on slopes. The example of a 3D spherical toppling slope was reconstructed and corroborated by calculation. The experimental results demonstrated that the proposed method could appropriately reflect the mechanical properties and stability behaviour of a 3D toppling slope, thereby facilitating the 3D stability analysis of toppling rock slopes.

3D stability analysis of tunnel face with influence of unsaturated transient flow

The analysis of tunnel face stability is commonly implemented with the assumption that the soil is dry or fully saturated. However, many practical cases occur in partially saturated soils, and the unsaturated component of the shear strength warrants consideration for a more realistic solution. This paper extends the current understanding of the tunnel face stability, which, for the first time, incorporates the contributions of unsaturated transient flow into the analytical framework of the three-dimensional (3D) tunnel face stability. A closed-form describing the spatio-temporal variability of saturation, suction stress, and apparent cohesion was derived and introduced into the Mohr-Coulomb criterion to consider the unsaturated transient flow. Within the framework of the kinematic approach of limit analysis, the work rate balance equation including the unsaturated component was established based on a 3D horn-like failure mechanism. A parameter analysis concerning the hypothetical fine sand, silts, and clay was performed to study some parameters of interest. The results show that unsaturated transient flows play a positive role in reducing the required face pressure. The magnitude of the influence is controlled by factors including soil types, thickness of the soil layer, and infiltration time. Compared with neglecting the unsaturated effect, the reduction of normalized critical face pressure caused by transient flows can reach 16.22% in fine sands, 24.98% in silts, and 85.62% in clays. The results suggest that the contribution of unsaturated transient flow to clays, particularly in the early infiltration stage, should be considered. Findings of this work can provide an insight to quantitively capture the influence of the unsaturated transient infiltration and the resulting transient changes of the 3D tunnel face stability.