Sloping Layer Research Articles

The influence of toe geometry on toe armour stability for conventional rubble mound breakwaters

Rubble mound breakwaters have toe structures that provide support to the armour layer and prevent damage to the structure from scouring. In this way, toe failure may be regarded as one of the primary failure modes of rubble mound breakwaters. Several formulae have been proposed for toe stability with conflicting results owing to the neglect of factors such as storm duration and armour layer slope. In the present study, a statically stable rubble mound with rock armoured toe was tested under irregular waves. The effects of wave height, wave period, armour layer slope, water height in front of the structure, water height above the toe, and toe width on the hydraulic stability of a toe structure are investigated. Toe width was found to be ineffective on toe stability, while the relative depth was found as an effective parameter for the toe stability. Greater toe damage was observed by increasing wave height and storm duration. The results highlighted the necessity for a new stability number involving the type of wave breaker on the armour slope with a critical Iribarren value of 4.1. Based on the data from the present study and the findings of another study, new formulae have been developed for estimating toe damage in rubble mound breakwaters. Evaluating the proposed formula using other researchers’ data and formulae highlighted its strengths.

Effects of a surface layer cross-flow and slope steepness on the rate of descent of dense water flows along a slope

The pathways and mixing in dense water overflows have been addressed in a range of numerical studies based on the DOME (Dynamics of Overflow Mixing and Entrainment) setup. These studies are motivated by overflows such as the flow of dense and cold water over the ridge between Iceland and Scotland. The main route of this water is through the Faroe-Shetland channel and further through the Faroe Bank Channel. After leaving the Faroe Bank Channel, the dense water continues along the slope along the Iceland-Faroe Ridge. Across this ridge there is also a strong flow of Atlantic water that may affect the pathway and mixing in the dense plume. In the DOME investigations, the slope steepness is assumed to be constant and there is no active background flow in the ambient water masses above the dense plume. With the situation along the Iceland-Faroe Ridge in mind, the setup from the DOME experiment is adjusted to study the effects of i) the slope profile, ii) flows crossing the slope on top of the along-slope flow of dense water, and iii) the topography near the overflow channel of dense water. It is found that the rate of descent is depending on slope steepness, and for a curved slope going from flat on top of a ridge to much steeper away from the ridge, dense water parcels near the ridge top or crest will sink slower than the faster flowing dense water further down along the slope. A cross-flow over the ridge, mimicking the flow of Atlantic water over the Iceland-Faroe Ridge, will force stronger mixing between the dense water and the ambient water above and dense water mixed up into the surface water can be allowed to flow out across the ridge. Furthermore, the dynamical situation along the slope will change and fluid parcels in the deeper part of the plume can experience a faster rate of descent. By removing a barrier in the topography downstream of the overflow channel, dense water can be steered towards the ridge and the starting point of the center of mass of the descending overflow water will be higher up on the slope.

Theoretical and experimental modeling of geodynamiс processes in uplift slopes

The flow structure created in a viscous medium at a constant inclination angle of the free surface of the uplift slope is analyzed. The velocity field in a high-viscosity uplift slope is determined under conditions of a horizontal pressure gradient. This pressure gradient occurs when the slope height decreases with distance from the main ridge. With a constant dynamic viscosity of the uplift slope, the flow velocity in it decreases with distance from the axis of the main ridge. In this case, the uplift slope is in conditions of compressive stresses, the consequence of which are thrusts and compression folds. Tensile stresses in the uplift slope exist with an increase in the flow velocity in the layer with distance from the main ridge axis. The flow velocity increases with decreasing viscosity of the layer with distance from the main ridge. The viscosity distribution on the base of the uplift slope at a distance from the axis of the main ridge is determined using the tension condition in the uplift slope. Expressions are presented for the forces causing the formation of a disruption between the blocks of the uplift slope. The magnitudes of these forces are estimated. A relation representing the condition for the formation of a disruption between the blocks is obtained. The formation of disruptions is governed by the change in viscosity along the uplift slope and the change in the flow velocity in it. When the disruption between the uplift slope is formed, free vertical boundaries of the blocks appear. The motion of a highly viscous liquid during the formation of a free vertical boundary of the block has been studied experimentally when the liquid flows out from a rectangular vessel. The experiments have revealed two outflow regimes: (i) the regime of constant thickness of the liquid layer; (ii) the regime of decreasing layer thickness. On the basis of experimental modeling the time of the first period after the formation of the slope rupture and the formation of the free volume between the blocks is estimated. During this period the height of the layer (slope) is practically constant and the layer length increases. The process of filling the free volume between the blocks with a high-viscosity slope material is considered. As the modeling shows, the filling rate of the free volume between the diverging blocks of the uplift slope is much higher than the formation rate of the free volume between these blocks. The parameters of the uplift slope blocks are determined. Among these parameters are block viscosity, slope height, flow velocity and forces acting on the blocks. The time-varying structure of the surface of the uplift slope is presented. There is a qualitative correspondence between the modeling results and the profile of the uplift slope for the north-western Caucasus.

Seismic response and damage evolution process of a bedded slope‒tunnel system via the continuum‒discontinuum element method

To investigate the failure evolution process and failure mechanism of the bedded slope‒tunnel system under earthquakes, this work examines a specific layered slope at a tunnel portal in southeast China and conducts a 2D dynamic analysis with the continuum‒discontinuum element method (CDEM). It investigates the slope's dynamic behavior and potential for instability by evaluating the wave patterns, acceleration, displacement, Hilbert‒Huang transform (HHT) spectral analysis, and equivalent crack ratio. The research results indicate that the analysis of acceleration and displacement over time provides insights into wave propagation within a slope. During minor earthquakes (< 0.3 g), the slope experiences dynamic amplification at the surface and elevation-dependent effects, which are less evident during stronger seismic events. This work also revealed a positive correlation between the tunnel's dynamic amplification and elevation. A method leveraging HHT energy analysis, in conjunction with the slope's equivalent fracture ratio, is introduced to trace the progression of seismic damage across temporal and spatial dimensions. The progression of seismic intensity is characterized by stages of local failure initiation, expansion, and eventual holistic failure. Similarly, the temporal dynamics of instability are categorized into phases of initial instability, acceleration, and eventual sliding. Furthermore, this work explores the impact of tunnels on slope stability by comparing the equivalent fracture ratios and dynamic displacement patterns of slopes both with and without tunnels, revealing the evolution process of seismic damage to slope‒tunnel systems. This work provides a reference for the seismic design of complex slope‒tunnel systems.

Modeling spatial variability of mechanical parameters of layered rock masses and its application in slope optimization at the open-pit mine

Mining engineering with layered structures often obtains extensive geological data to ensure reliability of mining operations. Effectively utilizing these data to characterize the spatial distribution of mechanical parameters in layered rock mass is crucial for slope stability analysis. This study focuses on the Heishan open-pit mine as a case study, leveraging the distinctive characteristics of mining engineering geological data. A three-dimensional fracture network was then generated based on the distribution of fractures in the rocks, and the representative elementary volume of the rock mass was determined by calculating the volumetric joint count (Jv). Statistical characteristics of various geological data are analyzed, and a geological statistical method combining the Kriging method and inverse distance power method is applied to establish a spatial distribution block model for geological strength index (GSI) and rock mechanical properties. Subsequently, a spatial variability model of the mechanical parameters of the layered rock mass was generated based on the Hoek–Brown criterion. Furthermore, the heterogeneous mechanical model is implemented in numerical software for stability analysis and slope angle optimization. The findings indicate that each engineering zone of layered slopes exhibits unique mechanical parameters while demonstrating significant layered distribution patterns at a macro level. Considering spatial variability, the mechanical model significantly impacts slope stability and slope angle optimization outcomes. Our research methodology facilitates accurate quantification of the heterogeneity of mechanical parameters in layered slopes without incurring excessive additional survey costs, enabling more rational explanations of slope landslides and the provision of suitable slope angle optimization designs.

Shaking Table Test Study of Dynamic Response and Failure Mode of Liquefiable Layer Slope Under Earthquake

As a kind of special terrain, the landslide disaster generated by liquefiable layer slopes under earthquake has become a major engineering challenge due to its large scale and long slip distance. In order to study the seismic response and damage mode of liquefiable layer slope, this paper follows the research line of “geological generalization, physical modeling, and result analysis”, and takes the liquefiable layer slope in the upper reaches of the Yellow River Class secondary terrace as the object of study, generalizes the physical model of the slope, and carries out shaking table test. Based on the PGA amplification coefficient, Fourier analysis and HHT time–frequency characterization of the model slope, it was found that the PGA amplification coefficient increases gradually along the slope height, reaches the maximum value at the top of the liquefiable layer and then decreases gradually, which indicates that the liquefiable sand layer has an obvious energy dissipation effect, and on the horizontal direction of model slope is a tendency to the surface effect; the seismic waves at the discontinuous interface change drastically, and the Hilbert time–frequency spectrum transforms from multiple peaks to a single peak; with the increase of the intensity, the intrinsic frequency of the overall model decreases, and the high-frequency component within the liquefiable sand layer decreases from 5–15[Formula: see text]Hz to 0–5[Formula: see text]Hz, indicating that the liquefiable layer has a filtering effect; the damage process of the liquefiable layer slope is the tensile crack at the top of the slope — seismic subsidence at the top of the slope — the shear yielding at the angle of the slope — shear surface penetration at the slope face — overall slope instability and flow-slip damage. The research results will provide a reference for the study of the disaster mechanism of the liquefiable layer slope.

Correction: Investigating Toppling Failure Mechanism of Anti-dip Layered Slope due to Excavation by Physical Modelling

Correction: Investigating Toppling Failure Mechanism of Anti-dip Layered Slope due to Excavation by Physical Modelling

Upper Bound Analysis of Two-Layered Slopes Subjected to Seismic Excitations Using the Layer-Wise Summation Method

Due to natural sedimentation and artificial filling, slopes exhibit heterogeneity in the form of multi-layer soils, namely, layered slopes. Compared with homogenous slopes, the failure mechanism of layered slopes is more complex owing to the different shear strengths of each soil layer. Therefore, it is of great importance to gain insight into the stability of layered slopes. In this study, the upper bound theorem of limit analysis incorporated with a pseudo-static approach is utilized to investigate the seismic stability of two kinds of two-layered slopes: one with a stiff lower soil layer and the other with a weak lower soil layer. Three failure patterns, namely face failure, toe failure and base failure, are taken into account. A depth coefficient (Δ) is introduced to describe the distribution of two soil layers. The layer-wise summation method is adopted to calculate the safety factor and yield acceleration coefficient more conveniently. Based on Newmark’s method, the earthquake-induced horizontal displacement is estimated. The calculated results are validated by comparisons with published literature and the numerical method in terms of safety factor, critical failure surface and yield acceleration coefficient. The results show that the depth coefficient has a significant influence on the failure mechanism of two-layered slopes by determining whether the stability of upper-layered soil is dominant in the overall slope stability or not. Inaccurately identifying the failure patterns will overestimate the seismic performance of two-layered slopes in the aspects of safety factor and yield acceleration coefficient, leading to an underestimation of earthquake-induced horizontal displacement.

Energy Dynamic Characteristics of Seismic Wave Propagation in Bedrock and Overburden Layer Slope

Energy Dynamic Characteristics of Seismic Wave Propagation in Bedrock and Overburden Layer Slope

Profiles of suction stress of layered soils under infiltration conditions and its applications

Suction stress is critical for understanding the hydrological and mechanical behavior of unsaturated soils in construction and engineering. Many soils encountered in these fields exhibit layering due to geological sedimentation or artificial reinforcement. This study establishes the vertical distributions of matric suction and degree of saturation for layered soils under one-dimensional (1D) steady-state seepage, using the Darcy law and constitutive relationships of unsaturated soils. A closed-form suction stress is derived for an arbitrary number of layers and soil types. Hypothetical layered soils with varying hydraulic properties at four infiltration rates are assessed. Results show that soil stratification affects the suction stress profiles, with the impact depending on infiltration rates, soil configuration, and layer thickness. Abrupt variations in suction stress occur at most layered interfaces due to differences in permeability between adjacent layers. The suction stress profiles can be used to evaluate the earth pressure and stability of layered slopes under seepage conditions. Several case studies of multi-layered slope failures in Southern Italy are presented to demonstrate the suitability of the proposed framework for evaluating the stability of layered slopes under rainfall conditions.

Stability analysis of layered circular rock tunnels considering anchor reinforcement based on an enhanced mesh-free method

The impact of geotechnical structure and support construction on the stability of a layered circular rock tunnel was investigated based on an improved mesh-free method. The Smoothed Particle Hydrodynamics (SPH) was improved by incorporating a total bridge broken strategy into the kernel function and was validated through analysis of the mechanical behavior in circular opening problem and uniaxial compression tests. The Particle Domain Search (PDS) method is utilized to create crack pathways and implement anchor reinforcement in specific areas without the requirement for grid division. An SPH model of the Muzhailing tunnel was established to investigate the stability of the surrounding rock considering different anchor lengths and spacing. The result indicated that the enhanced SPH method provides a feasible approach for the rapid assessment of tunnel convergence displacement and damage coefficients. Furthermore, this method was validated through laboratory experiments and analytical solutions. For layered tunnels with other different dip angles, this approach offers a general optimization strategy for anchor reinforcing surrounding rock. These findings suggest that the enhanced mesh-free method, owing to its characteristics of efficient parameter calibration and computation, can be further expanded to the rapid assessment of the stability of layered slopes and foundations considering anchor reinforcement.

Seismically induced deformations of layered slopes with non-unique and non-planar slip surfaces

Earthquake-induced deformation is prevalently used to evaluate the seismic performance of slopes, often assumed to occur along a predefined single slip surface. This paper presents a new limit equilibrium method combining with Newmark sliding block analysis for calculating the seismic displacement of layered slopes with non-unique and non-planar slip surfaces. The determination of the most and subsequent critical slip surfaces during the earthquake shaking is discussed with an emphasis on the coupling effects between the shallow and deep failures. The approach is validated by the results from numerical simulation and the shaking table model test of layered slopes. Comparison analyses are also performed for the predictions of seismic displacement from the developed and previous sliding-block models. It is found that the seismic sliding deformation at the first slip surface significantly affects the evolution and sliding deformation of the subsequent slip surface. For the considered example of layered slope, a second slip surface at deeper location passing through the slope toe is identified, and a coupled variation is observed for the sliding displacement along the two slip surfaces. These features are not well predicted from the available sliding-block models. The developed model can capture the interaction between the non-unique slip surfaces and the geometry effect of the non-planar slip surfaces.

Shaking table test on damage mechanism of bedrock and overburden layer slope based on the time–frequency analysis method

To systematically analyze the damage caused by bedrock and overburden layer slope under seismic action, a set of large-scale shaking table test was designed and completed. Interpolation of the acceleration amplification coefficient, Hilbert–Huang transform and transfer function was adopted. The damage mechanisms of the bedrock and overburden layer slopes under seismic action are systematically summarized in terms of slope displacement, acceleration field, vibration amplitude, energy, vibration frequency, and damage level. The results show a significant acceleration amplification effect within the slope under seismic action and a localized amplification effect at the top and trailing edges of the slope. With an increase in the input seismic intensity, the difference in the vibration amplitude between the overburden layer and bedrock increased, low-frequency energy of the overburden layer was higher than that of the bedrock, and the vibration frequency of the overburden layer was smaller than that of the bedrock. These differences cause the interface to experience cyclic loading continuously, resulting in the damage degree of the overburden layer at the interface being larger than that of the bedrock, reduction of the shear strength, and eventual formation of landslides. The displacement in the middle of the overburden is always greater than that at the top. Therefore, under the action of an earthquake and gravity, the damage mode of the bedrock and overburden layer slope is such that the leading edge of the critical part pulls and slides at the trailing edge, and multiple tensile cracks are formed on the slope surface.

Probabilistic stability analysis of a layered slope considering multi-factors in spatially variable soils

Probabilistic stability analysis of a layered slope considering multi-factors in spatially variable soils

Stability Analysis of Seismic Slope Based on Relative Residual Displacement Increment Method

The seismic stability analysis of a slope is a complex process influenced by earthquake action characteristics and soil mechanical properties. This paper presents a novel seismic slope stability analysis method using the relative residual displacement increment method in combination with the strength reduction method (SRM) and the actual deformation characteristics of the slope. By calculating the relative displacement of the key point inside the landslide mass and the reference point outside the landslide mass after each reduction, the safety factor of the slope is determined by the strength reduction factor (SRF) corresponding to the maximum absolute value of the relative residual displacement increment that appears after a continuous plastic penetration zone. The method eliminates interference caused by significant displacement fluctuations of key points under earthquake action and reduces the subjective error that can occur when manually identifying displacement mutation points. The proposed method is validated by dynamic calculations of homogeneous and layered soil slopes and compared with three other criteria: applicability, accuracy, and stability.

Deformation Patterns and Failure Mechanisms of Soft-Hard-Interbedded Anti-Inclined Layered Rock Slope in Wolong Open-Pit Coal Mine

Since the beginning of spring 2022, successive landslides have occurred in the eastern pit slope of the Wolong Coal Mine in Qipanjing Town, Otog Banner, Inner Mongolia, which has adversely affected the mine’s production safety. This study aims to reveal the deformation patterns and failure mechanisms of landslides. Firstly, this study establishes the stratigraphic structure of the eastern pit slope of the Wolong Coal Mine using extensive field geological surveys combined with unmanned aerial vehicle photography, drilling, and comprehensive physical exploration techniques. Indoor geotechnical tests and microscopic experiments reveal that rock mass typically exhibits the characteristics of expansibility and water sensitivity. Moreover, the mechanical parameters of the rock mass were determined using a combination of the window sampling method, the Geological Strength Index, and the Hoek–Brown strength criterion estimation theory. Finally, this study consolidates the previously mentioned insights and employs FLAC3D (7.0) software to assess the stress–strain characteristics of the excavated slope. The results indicate that the deformation mode of the Wolong open pit coal mine is the toppling failure of soft-hard-interbedded anti-inclined layered rock slopes. The unloading effect and rock expansion-induced softening lead to stress concentration at the slope corners and more substantial deformation, thereby accelerating upper slope deformation. The deformation and destabilization process of landslides is categorized into four stages: the initial deformation stage, the development stage of lateral shear misalignment, the development stage of horizontal tensile-shear damage, and the slip surface development to the preslip stage. This research offers valuable references and engineering insights for future scientific investigations and the prevention of similar slope-related geological hazards.

Evaluation of liquefaction‐induced lateral spread displacement based on ensemble learning

Liquefaction‐induced lateral spread is a kind of ground deformation caused by soil liquefaction, which is a danger to houses, roads and other infrastructures. In order to systematically investigate the influence law of different parameters on lateral displacement, this paper establishes a numerical model of the seismic responses of gently sloping grounds through the open‐source finite element software OpenSees and carries out a large number of calculations considering various working conditions. Based on the calculation results, eXtreme Gradient Boosting (XGBoost) and random forest (RF) regression are used to build the proxy models for lateral spread displacement prediction. The finite element model was verified by using the multiple VELACS No. 2 centrifuge experiments. Finally, the model was interpreted using SHapley Additive exPlanation (SHAP) method. The results of the model training showed that both models were able to achieve a good fit to the numerical calculation results, with the RF model having a smaller prediction error for the centrifuge experiments. The model interpretation results showed that the modified cumulative absolute velocity (CAV5) was the most important input variable in the model, and the importance of ground slope (S), relative density (Dr) and thickness of liquefiable soil layer (HL) was relatively high. In addition, the influence of each parameter on the lateral displacement is consistent with the actual situation, reflecting the rationality of the model prediction process. In addition, the results showed that there is a threshold for the modified cumulative absolute velocity (CAV5) and Arias intensity (Ia) that leads to a significant increase in lateral displacement. The thresholds of CAV5 and Ia are 1.3 g s and 1.0 m/s, respectively. These thresholds are in good agreement with the thresholds for triggering the overall initial liquefaction of the soil layer determined by related studies, which provides a reference for the evaluation of liquefaction‐induced lateral displacement.

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

Study on Slope Monitoring and Stability Based on Bolt–Cable Combined Support

To provide reference for the design and construction of anchoring measures in slope reinforcement and treatment projects, this article presents the on-site monitoring and analysis of the stress changes in anchor rods and anchor cables in a high-level layered rock slope of a deep excavation highway. Anchor rods and anchor cables are widely used reinforcement measures in slope reinforcement due to their simplicity and economy. In this article, we took the layered rock slope of a deep excavation highway as the monitoring object and installed monitoring equipment on slopes of different levels. Based on the monitoring data of slope anchor rods and anchor cables, the rationality of slope reinforcement and treatment measures was analyzed. This study shows that active support anchor cables have better reinforcement effects than the passive protection of anchor rods. The approximate position of the potential slip surface in the slope mass can be inferred according to the monitoring of slope anchor stress, which can guide a slope reinforcement and treatment project. Finally, FLAC3D V6.0 was used for numerical simulation analysis, which showed that the slope was in a stable state under the support of anchor rods and anchor cables.

Case study on long-term deformation monitoring and numerical simulation of layered rock slopes on both sides of Wudongde dam reservoir area

Layered rock slope exists widely. Because of its special slope structure, it is prone to bending deformation and toppling failure, which is a serious threat to engineering construction and safety operation. At present, the research of layered rock slope still has great innovation potential. During the construction of Wudongde Hydropower Station on Jinsha River, safety and stability problems such as slope geological structure development, face rock unloading and relaxation, and even slip and large deformation were encountered. Through field exploration, it is found that the rock and soil stratification of the slope on both sides of Wudongde Hydropower Station is highly obvious. At present, there is a lack of research on-site long-term displacement monitoring of layered rock high-steep slope, especially for layered slope in complex hydrogeology and construction environment. In order to strengthen the research on the deformation and stability of layered rock slope, this paper analyzes the measured displacement data of Wudongde hydropower station slope, and establishes three-dimensional geological finite element model with the help of numerical simulation software. The stability of the slope is calculated by combining the finite difference method and the strength reduction method. Finally, the evolution mechanism of the deformation of the layered rock slope is explained according to the geological structure characteristics. The main conclusions of this paper are as follows: the layered slope in the dam reservoir area is prone to deformation under the combined action of long-term construction disturbance and fissure water seepage, and the construction disturbance has a strong influence on the artificial excavation area below 1070 m, and the maximum rock mass deformation and surface displacement in the artificial excavation area of the slope reach 92.2 mm and 312.5 mm, respectively. However, the influence of construction disturbance on the natural mountain above 1070 m is limited, the valley deformation of the natural mountain on the left bank of the reservoir area is higher than that on the right bank, and the cumulative deformation is still less than 20 mm. The influence of seepage on the displacement of the area with higher elevation at the top of the slope is more obvious, and the influence of excavation and other disturbances on the displacement of the artificial excavation area with lower elevation is more obvious. The deformation of the river valley in the water cushion pond behind the dam increases slowly, and the change trend of the field deformation data is mostly consistent with that of the numerical calculation. The horizontal shrinkage of the mountains on both sides shows a contraction trend on the whole, and the maximum horizontal shrinkage calculated by numerical simulation is close to 20 mm, which is located at the elevation of 990 m.