Increasing Slope Angle Research Articles

Numerical Investigation of the Slope Stability in the Waste Dumps of Romanian Lignite Open-Pit Mines Using the Shear Strength Reduction Method

Open-pit mining generates significant amounts of waste material, leading to the formation of large waste dumps that pose environmental risks such as land degradation and potential slope failures. The paper presents a stability analysis of waste dump slopes in open-pit mining, focusing on the Motru coalfield in Romania. To assess the stability of these dumps, the study employs the Shear Strength Reduction Method (SSRM) implemented in the COMSOL Multiphysics version 6 software, considering both associative and non-associative plasticity models. (1) Various slope angles were analyzed, and the Factor of Safety (FoS) was calculated, showing that the FoS decreases as the slope angle increases. (2) The study also demonstrates that the use of non-associative plasticity leads to lower FoS values compared to associative plasticity. (3) The results are visualized through 2D and 3D models, highlighting failure surfaces and displacement patterns, which offer insight into the rock mass behavior prior to failure. (4) The research also emphasizes the effectiveness of numerical modeling in geotechnical assessments of stability. (5) The results suggest that a non-associative flow rule should be adopted for slope stability analysis. (7) Quantitative results are obtained, with small variations compared to those obtained by LEM. (6) Dilatation angle, soil moduli, or domain changes cause differences of just a few percent and are not critical for the use of the SSRM in engineering.

The influence of rainfall patterns on factor of safety for clayey soil slopes

The persistent trend of rising temperatures and shifting weather patterns caused by climate change has prompted significant concern around the world. This research aims to evaluate the instability of slopes in Almaty, Kazakhstan, under various rainfall patterns, groundwater tables, and slope geometries by incorporating the principles of unsaturated soil mechanics. However, there have been a limited number of studies incorporating the principle of unsaturated soil mechanics with constant rainfall patterns in Central Asia, particularly in Kazakhstan, on the impact of rainfall-causing landslides. Hence, in this research, GeoStudio software (SEEP/W and SLOPE/W) was used to simulate the factor of safety (FoS) and pore water pressure for the investigated slopes under different rainfall patterns. Results from Hyprop and statistical method show that the saturated volumetric water content is 0.502, whereas the residual one is 0.147 and for the permeability function the conductivity coefficient started to sharply decrease at the suction value of 2 kPa when the air-entry value was 24 kPa. Findings from numerical analysis show the change in FoS for the slope of 10 m height and 27-degree slope angle was 6%, 7%, 7%, and 8% for cyclic, delayed, advanced, and normal distributions, respectively. For the slope with 20 m height and the same 27-degree angle, the change in FoS was 8%, 10%, 8%, and 11% for the cyclic, delayed, advanced, and normal distributions, respectively. These same patterns were shown in slopes with 35-degree and 45-degree angles, having the same 10 m and 20 m heights. Comparatively, this shows that slopes under cyclic rainfall patterns (240 mm of rain within 12 days) are less prone to failure compared to slopes under continuous, delayed, or regularly distributed rainfall patterns. Moreover, an increase in slope height and angle also affect the FoS negatively. It should be noted that the results obtained are only applicable to clayey-loam soil.

Effect of slope angle on fractured rock masses under combined influence of variable rainfall infiltration and excavation unloading

Intense precipitation infiltration and intricate excavation processes are crucial factors that impact the stability and security of towering and steep rock slopes within mining sites. The primary aim of this research was to investigate the progression of cumulative failure within a cracked rock formation, considering the combined effects of precipitation and excavation activities. The study was conducted in the Huangniuqian eastern mining area of the Dexing Copper Mine in Jiangxi Province, China. An engineering geological investigation was conducted, a physical model experiment was performed, numerical calculations and theoretical analysis were conducted using the matrix discrete element method (MatDEM), and the deformation characteristics and the effect of the slope angle of a fractured rock mass under different scenarios were examined. The failure and instability mechanisms of the fractured rock mass under three slope angle models were analyzed. The experimental results indicate that as the slope angle increases, the combined effect of rainfall infiltration and excavation unloading is reduced. A novel approach to simulating unsaturated seepage in a rock mass, based on the van Genuchten model (VGM), has been developed. Compared to the vertical displacement observed in a similar physical experiment, the average relative errors associated with the slope angles of 45°, 50°, and 55° were 2.094%, 1.916%, and 2.328%, respectively. Accordingly, the combined effect of rainfall and excavation was determined using the proposed method. Moreover, the accuracy of the numerical simulation was validated. The findings contribute to the seepage field in a meaningful way, offering insight that can inform and enhance existing methods and theories for research on the underlying mechanism of ultra-high and steep rock slope instability, which can inform the development of more effective risk management strategies.

Study on the differences between Hoek–Brown parameters and equivalent Mohr–Coulomb parameters in the calculation slope critical acceleration and permanent displacement

Mohr–Coulomb (MC) strength criterion has been widely used in many classical analytical expressions and numerical modeling due to its simple physical calculation, but the MC criterion is not suitable for describing the failure envelope of rock masses. In order to directly apply MC parameters to analytical expressions or numerical modeling in rock slope stability analysis, scholars established a criterion for converting Hoek–Brown (HB) parameters to equivalent MC parameters. However, the consistency of HB parameters and equivalent MC parameters in calculating critical acceleration of slope needs to be further explored and confirmed. Therefore, HB parameters are converted into equivalent MC parameters by considering the influence of slope angle (1# case and 2# case when slope angle is not considered and slope angle is considered respectively). Then, the lower-bound of finite element limit analysis is used for numerical modeling, and the results of calculating critical acceleration using HB parameters and equivalent MC parameters are compared, and the influence of related parameters on the calculation of critical acceleration is studied. Finally, the influence of different critical accelerations on the calculation of slope permanent displacement is further analyzed through numerical cases and engineering examples. The results show that: (1) In the 1# case, the critical acceleration obtained by the equivalent MC parameters are significantly larger than that obtained by the 2 #case and the HB parameters, and this difference becomes more obvious with the increase of slope angle. The critical acceleration obtained by the 2# case is very close to the HB parameters; (2) In the 1# case, slope height is inversely proportional to ΔAc (HB(Ac) − 1#(Ac)), and with the increase of slope height, ΔAc decreases, while in the 2# case, the difference of ΔAc (HB(Ac) − 2#(Ac)) is not significant; (3) In the 1# case, the sensitivity of the HB parameters to ΔAc is D > GSI > mi > σci, but in the 2# case, there is no sensitivity-related regularity; (4) The application of HB parameters and equivalent MC parameters in slope permanent displacement is studied through numerical cases and engineering examples, and the limitations of equivalent MC parameters in rock slope stability evaluation are revealed.

Ultimate Pit Limit Optimization Method with Integrated Consideration of Ecological Cost, Slope Safety and Benefits: A Case Study of Heishan Open Pit Coal Mine

The ecological impacts of mining and the instability of slopes are the key factors restricting the safe, efficient, and low-carbon production of open-pit mines. This study focused on the ultimate pit limit (UPL) optimization under the concept of sustainability by integrating consideration of the economic benefit, ecological impact, and slope geometry. The integrated UPL optimization model based on the floating cone method was proposed by establishing a quantitative model for ecological impacts arising from open-pit coal mining in arid or semi-arid weak ecological land and a cost calculation model of slope reinforcement based on the Monte Carlo method. The case study revealed that steepening the slope angle of given regions resulted in random variations in the quantity of ore rock and the limit morphology. There was an average economic profit rise of USD 9.54M with every 1° increase in slope angle, but the probability of slope instability and the reinforcement cost grows exponentially. In the arid or semi-arid weak ecological land, the ecological costs exceeded 20% of the mines’ average pure economic gains. The proposed optimization method contributes to obtaining an integrated optimal UPL, improving the benefits and the ore recovery rate.

Stability analysis of rainfall-induced landslide considering air resistance delay effect and lateral seepage

Accumulation landslides are prone to occur during the continuous infiltration of heavy rainfall, which seriously threatens the lives and property safety of local residents. In this paper, based on the Green-Ampt (GA) infiltration model, a new slope rainfall infiltration function is derived by combining the effect of air resistance and lateral seepage of saturated zone. Considering that when the soil layer continues to infiltrate after the saturation zone is formed, the air involvement cannot be discharged in time, which delays the infiltration process. Therefore, the influence of air resistance factor in soil pores is added. According to the infiltration characteristics of finite long slope, the lateral seepage of saturated zone is introduced, which makes up for the deficiency that GA model is only applicable to infinite long slope. Finally, based on the seepage characteristics of the previous analysis, the overall shear strength criterion is used to evaluate the stability of the slope. The results show that the safety factor decreases slowly with the increase of size and is inversely correlated with the slope angle and initial moisture content. The time of infiltration at the same depth increases with the increase of size and slope angle, and is inversely correlated with the initial moisture content, but is less affected by rainfall intensity. By comparing with the results of experimental data and other methods, the results of the proposed method are more consistent with the experimental results than other methods.

Gait Factor on the Energy Harvesting for a Simple Biped Robot

To design walk-fast and energy-efficient robots, there has been lots of work in the last decade examining the locomotion dynamics of a passive biped. As the walking environment or system parameter changes, an energy use efficient robot may become inefficient. A possible approach to increase the energy efficiency is through the ability to harvest the energy used during the locomotion. The paper’s main goal is to investigate the relations between walking speed, the locomotion energy consumption of a passive biped, and the ability to retrieve the lost energy as locomotion energy efficiency varies. Piezoelectric bimorphs were attached to the feet of the biped to harvest energy via exploiting the acceleration excitations induced vibrations at the instant foot lift and heel strike. It is found that as a foot-to-hip mass ratio increases, the stable periodic-1 (P1) walking gait becomes slower and more energy costing. Also it means more available energy to harvest, although the retrieved energy is much smaller compared to the locomotive energy. Once the foot-to-hip mass ratio passes the periodic doubling (PD) point, P1 walking gaits will become limped P2 walking gaits, and the high energy cost situation alleviates, which also means less available energy to harvest. On the other hand, if the foot-to-hip mass ratio is fixed and the slope angle increases, the walking will experience sequences of PD bifurcations, and the walking gaits go through P1, P2, P4, P8, and chaotic walking. As the walking gaits change, the average walking efficiency, average locomotion energy consumption, and average harvested energy grow as the slope becomes deeper.

Soil Moisture Sensor-Based Landslide Monitoring: A Laboratory-Based Approach for Guwahati City

Various techniques for landslide mapping, monitoring and modelling are being employed in a variety of studies to keep people safe from landslides. Guwahati, a city in Assam (India) is surrounded by hills, with varied slope angles, become prone to landslide during monsoon season. Relative increase in the moisture content of soil is a major parameter for determining the occurrence of landslides that are induced by rainfall. An experimental model with varying slope angles is demonstrated to witness some proportionality behaviour of soil moisture value for the collected soil sample from landslide prone areas. The soil moisture sensor value increases with increase in slope angle. The toe position of moisture value also shows a significant display of data during landslide. This early warning module can be incorporated with the help of Blynk Application to send messages to the residents of landslide prone areas. This study would be a cost effective alternative for landslide early warning hazard monitoring and fast emergency response process and the model may be considered as a miniature version of real-life slope conditions for the hills of Guwahati city, Assam, India.

Slope Stability Analysis of Mounded Storage Tank under Different Compaction Coefficients

Mounded storage tank is to cover the storage tank with compacted soil on the ground to avoid steam cloud explosion, ensuring the stability and safety of the storage tank. In view of the influence of large diameter and surface radian of the tank, slope stability of mounded storage tank under different compaction coefficients has become the focus of research. In this paper, a series of laboratory tests were carried out to obtain the physical and mechanical parameters of the soil samples collected from the overburden of one specific engineering project. On this basis, Plaxis2D finite element software was used to establish a numerical model of the horizontal tank with a diameter of 7.6 m and a length of 76 m and the mounded slope with a height of 16.25 m as the research object. The effects of different compaction coefficients, slope angles, and overburden thicknesses on the slope stability of the mounded storage tank are investigated. Results indicate that the slope stability coefficients increase with the increase of compaction coefficient but decrease with the increase of slope angle and overburden thickness. Under the condition of the compaction coefficient 0.75–0.95, slope angle 30°–60°, and overburden thickness 0.5–1.3 m, the sensitivity ranking on the slope stability of mounded storage tank is: compaction coefficient, slope angle, and overburden thickness. The analysis results can provide an important theoretical basis and technical support for the safety and stability evaluation of mounded horizontal tank project.

On the hydraulic performance of the inclined drops: the effect of downstream macro-roughness elements

Abstract The main goal of the present study is to investigate the effects of macro-roughnesses downstream of the inclined drop through numerical models. Due to the vital importance of geometrical properties of the macro-roughnesses in the hydraulic performance and efficient energy dissipation downstream of inclined drops, two different geometries of macro-roughnesses, i.e., semi-circular and triangular geometries, have been investigated using the Flow-3D model. Numerical simulation showed that with the flow rate increase and relative critical depth, the flow energy consumption has decreased. Also, relative energy dissipation increases with the increase in height and slope angle, so that this amount of increase in energy loss compared to the smooth bed in semi-circular and triangular elements is 86.39 and 76.80%, respectively, in the inclined drop with a height of 15 cm, and 86.99 and 65.78% in the drop with a height of 20 cm. The Froude number downstream on the uneven bed has been dramatically reduced, so this amount of reduction has been approximately 47 and 54% compared to the control condition. The relative depth of the downstream has also increased due to the turbulence of the flow on the uneven bed with the increase in the flow rate.

Numerical analysis of horizontal bearing capacity of pile in clay slope

In this study, a series of numerical calculations were performed to investigate the lateral behavior of piles in slopes and in horizontal ground. First, a numerical model is created and then verified by comparing the numerical results with the results of model tests. The numerical results agree well with the results of model tests. Second, numerical calculations of different slopes were conducted to explore the effect of slope angle on the horizontal displacement of pile and bending moment. Then, the effect of slope angle on the foundation stiffness proportional coefficient m is investigated. The stress distribution of soil around the pile and the deformation of pile at different slope angles are also compared. Finally, the p–y curves of the different slope angles are compared. An improved p–y method is proposed to consider the effect of slope angle based on the numerical results. The results show that the bearing capacity of piles decreases with an increase in slope angle. The horizontal displacement of pile nonlinearly decreases along the pile body with the depth of pile. The bending moment of piles increases along the pile body with an increase in pile depth, and until 0.5 times of the pile length, the bending moment reaches the maximum value. As the slope angle increases, the maximum of bending moment tends to decrease. The distance from the slope toe to the pile section has a little influence on the pile bending moment and horizontal displacement. With an increase in slope angle, the horizontal foundation coefficient m gradually decreases.

Numerical Investigation on Uplift Behavior for Pipelines Shallowly Buried in Sloping Ground

In practice, pipelines are inevitably buried in sloping ground, however, previous studies and guidelines of pipe-soil interaction mainly focus on level ground. In this study, the upward resistance-displacement curve for slopes with angles up to 20° was numerically investigated. To reflect the state-dependence, pre-peak hardening, and post-peak softening properties for dense sand, a modified Mohr-Coulomb model was implemented and validated by available physical tests. Numerical studies were carried out to explore the resistance-displacement curve, considering the coupling effects of slope angle, pipe-soil interface roughness, burial depth ratio. It is found that the pipeline in slopes is subjected to unbalanced lateral contact stress around its periphery. The pipeline and surrounding soil tend to move towards the slope toe during the uplift, especially for the perfectly smooth pipeline. As the slope angle increases, the peak resistance decreases for the perfectly smooth pipeline while increases for the perfectly rough one. Besides, the generally rough pipeline shows a quick post-peak reduction in the resistance. Possible mechanisms behind these phenomena were explored. Finally, considering the coupling effects of slope angle, interface roughness, burial depth ratio, a simplified method for the resistance-displacement curve based on the limit equilibrium method was proposed.

Experimental and Numerical Study of the Trench Fire Spread Rule over a Sloped Uniform Fuel Bed: Rate of Fire Spread, Flame Morphology, and Heat Flux

Trench fires on sloped terrain are always complicated due to the corresponding flame dynamics and heat transfer mechanisms. Flame attachment may increase the rate of fire spread (ROS) by enlarging the heating area of unburned vegetation. In addition, variations in radiative and convective heat flux are of great importance to fire behavior characteristics. In this work, trench fire tests under different slopes (θ) and inclined sidewalls (A) were performed by numerical simulations based on the Lagrangian Particle Model (LPM) and Boundary Fuel Model (BFM) in the Fire Dynamics Simulator (FDS) and small-scale experiments, and the ROS, flame characteristics, and radiative/convective heat flux of the fire front are discussed in detail. The results indicate that the flame tends to adhere to the fuel bed with increasing slope angle and sidewall inclination. In particular, the flame becomes fully attached with a greater pressure difference than the buoyancy, which is caused by the unequal air entrainment between the front and behind the flame. When A = 90°, the critical slope angle of the flame adhesion (from slight tilt to full attachment) is identified as ~20°. The ROS (θ ≤ 15°) predicted by the BFM and LPM are closer to the small-scale experiments. The heat fluxes based on the experiments confirm the predominant mechanism of radiative heat transfer in trench fires at low slopes (θ ≤ 20°). Furthermore, convective heat transfer is more significant than radiative and becomes the main heating mechanism for θ ≥ 20°.

An analytical solution for the dynamic response of a seawater‐sloping seabed‐bedrock system under an oblique incident SV wave

AbstractThe characteristics of seabed ground motion are the theoretical basis for the study of seawater‐soil‐structure interactions and seismic‐induced geological hazards. There are numerous offshore marine structures located on sloping seabeds. Therefore, the sloping seabed's seismic response requires to be investigated. Engineers and scholars are more interested in the SV waves because they carry more energy than the P waves in earthquakes. An analytical solution for the steady‐state response of the inclined seafloor under an oblique incident SV wave is offered. The impacts of the seafloor angle on the fluid pressure and displacement of the saturated sediment layer are investigated under different incident wave frequencies, incident angles, and thicknesses of the seawater layer and sediment layer. By observing along the seabed surface, we discovered that the slope angle might cause considerable variances between different positions even at a small site. While examining the seabed at varying depths, we discovered that the incline angle has distinct impacts on different areas of the seabed. It has an amplifying effect at some depths and a reducing effect at other depths. Generally, as the slope angle increases, the distinction between the responses of the inclined and horizontal seabed becomes more prominent. Especially when the incidence angle of the SV waves is near the critical angle, the impacts of the slope angle become more significant. Even if the horizontal seabed model is employed with the same seawater depth, it is not suitable for analyzing the seismic response of a sloping seabed. Otherwise, significant errors would arise.

Study on the influencing factors and evolution of loess bank collapse with physical modelling

BackgroundReservoir bank collapse in loess areas may lead to the siltation of reservoir and bank retreat. Therefore, the study of reservoir bank collapse has practical significance. Almost of the bank collapse width prediction method were based on the classical graphical method which do not consider the process of bank collapse. But practice shows that this method can overestimate the width of bank collapse. Meanwhile, there are few studies specifically focused on the collapse of loess bank slopes.MethodsTo improve the prediction method of loss bank collapse width, the influence of water depth, dry density and bank slope angle on loess bank collapse was studied by physical modelling. The bank collapse width and the morphology of the bank slope were recorded during the experiment.ResultsThe bank collapse width increases with the increase of water depth, increases with the increase of slope angle, and decreases with the increase of dry density. The modeling process shows that the loess bank collapse occurs firstly underwater, the erosion niche will be formed underwater, and then the above water slope is damaged. This process is repeated until the underwater accumulation slope reaches the stable state, and then bank collapse stops. After the bank collapse, the above water slope is polyline, while the underwater slope is curved. When the slope angle is less than 27°, the bank collapse will not occur, and when the slope angle is between 27° and 40°, the bank collapse type is abrasion type. When the slope angle is greater than 40°, the bank collapse type is dumping type or shear type. Based on this, the improved balanced alluvial accumulation approach was proposed, which considers the mechanical equilibrium of above water bank slope and the morphology of underwater slope. The new method can reflect the stage characteristics of loess bank collapse, which is more reasonable than the empirical graphical method.ConclusionsThe experimental results indicate that when predicting the width of loess bank collapse, it is necessary to combine the bank collapse width and process of bank collapse. The relevant conclusions have a certain role in exploring the mechanism of loess bank collapse and bank collapse prediction methods.

Analysis of Maximum Economic Length of Soil Nail for Slope Stability

Slope stability is of utmost importance in geotechnical engineering, necessitating effective reinforcement methods to mitigate failures. This study examined the advantages, limitations, and overall suitability of soil nails and cable anchors in stabilizing slopes. Numerical modeling and analysis were performed using the Rocscience Slide2 program. The study analyzed soil nails and cable anchors for slopes of 10 m to 60 m height, slope angle from 35° to 90°, and friction angle from 27° to 36°. The findings reveal that the maximum economic length of soil nails decreases as slip surface depth, slope height, and slope angle increase. Additionally, the friction angle of the soil has a negligible effect on the maximum economic length of the soil nail.

Моделирование обрушения горной породы

Introduction. At present, the study of the movement of falling rock (collapses of rocks), the causes of their occurrence, as well as their influence on other slope processes is an important field of research. These studies are based on both theoretical knowledge and experimental observations. Separately, it is necessary to highlight the methods of mathematical and computer modeling, which are widely used in cases where experimental data are not enough. The study of the influence of the slope angle and the slope height (on which the falling rock mass was located at the initial moment of time) on the affected area was made using the methods of mathematical and computer modeling. Materials and methods. Two-fluid model based on the continuum approach and the kinetic theory of granular gas was used for a theoretical study of the movement of falling rock along the slope. The model takes into account the fluidization of the falling mass flow, and its implementation does not require the use of powerful computing resources. The modeling results obtained using the two-fluid model were compared with the results of an experimental study on the collapse of dolomite particles (average diameter 5 mm) carried out in the laboratory. The values of the slope height varied from 35 cm to 86 cm, the values of the slope angle varied from 35 degrees to 53 degrees in accordance with the experimental data. The results and discussion. The graphs of the distance of the rock run after its collapse in the dependence of the slope height and the slope angle were plotted. It is found that the calculation results are in good agreement with the experimental data (the relative error does not exceed 11%) for relatively large values of the slope angle. The results of calculations of the distance of the rock run are somewhat overestimated relative to the experimental data for small values of the slope angle. It is found that the affected area of dolomite particles increases with increasing slope angle and slope height. It should be noted that the affected area depends more on the values of the slope angle than on the height of the slope. If the slope is steeper (the value of the slope angle is greater), than the affected area is greater. Conclusion. The calculation results obtained using the two-fluid model describe the experimental data of the rock collapse satisfactorily. The results of calculations of the distance of the rock run are in good agreement with the experimental data (the relative error does not exceed 11%) for relatively large values of the slope angle. It is found that the distance of the rock run after its collapse depends more on the values of the slope angle than on the height of the slope. Resume. The research results can be useful in estimating the distance of the rock run after its collapse, as well as in developing a methodology for assessing affected areas during rock falls. The direction of future research is to improve the two-fluid model based on the continuum approach and the kinetic theory of granular gas for describing of real rock falls.

Experimental study on the morphology of turbulent diffusion flames with different aspect ratios under slope conditions

In this paper, the morphology of turbulent diffusion flames with varying aspect ratios under slope conditions was investigated. A simulated fire source using propane gas with an area of 80 cm2 was utilized. The influences of slope angle and aspect ratio of the fire source on the flame tilt angle (between the plume centerline and the slope), flame length, and flame height were systematically studied. The aspect ratio of the fire source (L/W) was changed from 1 to 8, and the slope angle was changed from 0° to 40°. Results indicate that the presence of a slope causes asymmetrical air entrainment on both sides of the fire plume, causing a pressure difference that leads to a decrease in the flame tilt angle as the slope angle increases. Additionally, the flame length increases monotonically with the slope angle due to the enhanced component of thermal buoyancy along the slope. Under the same slope condition, the flame tilt angle and flame height (perpendicular to the slope) decrease as the aspect ratio increases. This phenomenon is attributed to the increased entrainment restriction effect of the slope on the fire plume. New models for calculating flame tilt angle, flame length, and flame height, which consider the slope angle and aspect ratio of the fire source were established by using the equivalent perimeter of plume entrainment. To further verify the reliability of the newly established models, reference data with wide heat release rate (6.15 kW–231 kW), different slope inclination angle (0°–80°), pool size (equivalent diameter: 9 cm–44.1 cm), and different fuels (propane, ethylene) were used to against with the predicted values of our correlations. It is found that the maximum error of all correlations is within 15–20%, their universality and accuracy are further verified.

Experimental and numerical study for seismic response of strip footing on slopes

The present study investigates the free-field response of slopes as well as the seismic response of strip footing on slopes. The small-scaled physical model tests (PMT) have been performed under one-directional excitation. The sinusoidal waves of different amplitudes and frequencies are applied at the base of the model. To examine the kinematic interaction between the footing and slope, a rigid strip footing is placed at the center of the slope. The free-field response of the slope as well as the seismic response of the footing on the slope from PMT is determined using digital image correlation (DIC). Two-dimensional finite element analysis (FEA) has been carried out to simulate the PMT results. No study has been reported in the literature considering both experimental and numerical work. Further, the effects of increasing load on the footing on slopes have not been examined yet. Results from PMT and FEA are found in good agreement. The maximum amplification is observed near the crest for free-field response of slope. For both horizontal ground surface and sloping ground, the maximum amplification occurs at the frequency of excitation. However, some small peaks at other frequencies are also observed for the sloping ground due to the reflection of waves from the sloping surface. The seismic settlement of strip footing is increased with the increase of slope angle, amplitude and frequency of the excitation. However, the seismic settlement decreases with the increase in footing width and edge distance of footing from the slope. For footing on slope, the maximum amplification is observed at the center of the slope. A large settlement of footing is observed when the footing is heavily loaded (e.g., 80% of the ultimate bearing capacity of footing).

Stochastic Finite Element Analysis of Root-Reinforcement Effects in Long and Steep Slopes

This article introduces a novel numerical scheme within the finite element method (FEM) to study soil heterogeneity, specifically focusing on the root–soil matrix in fracture treatments. Material properties, such as Young’s modulus of elasticity, cohesion, and the friction angle, are considered as randomly distributed variables. To address the inherent uncertainty associated with these distributions, a Monte Carlo simulation is employed. By incorporating the uncertainties related to material properties, particularly the root component that contributes to soil heterogeneity, this article provides a reliable estimation of the factor of safety, failure surface, and slope deformation, all of which demonstrate a progressive behavior. The probability distribution curve for the factor of safety (FOS) reveals that an increase in the root area ratio (RAR) results in a narrower range and greater certainty in the population mean, indicating reduced material variation. Moreover, as the slope angle increases, the sample mean falls within a wider range of the probability density curve, indicating an enhanced level of material heterogeneity. This heterogeneity amplifies the level of uncertainty when predicting the factor of safety, highlighting the crucial importance of accurate information regarding heterogeneity to enhancing prediction accuracy.