Three-dimensional Limit Equilibrium Research Articles

Sand deformation behavior around modified suction caissons during lateral loading and analytical method obtaining lateral bearing capacity

The modified suction caisson (MSC) is an innovative offshore wind turbine foundation. Model tests and numerical simulations were carried out to explore the sand deformation behavior around the MSC under lateral loading. The vertical displacements fitting method and the level bubble method were proposed obtaining the sand deformation range. Influences of the vertical load, loading eccentricity and external structure sizes were investigated. It was found that the shape of the sand surface deformation range in front of the caisson can be fitted by ellipse functions. In the limit state, the sand surface deformation ranges around both the MSC and the regular suction caisson (RSC) decrease with increasing loading eccentricity and vertical load. Besides, the sand surface deformation range in front of the MSC increases with increasing the external structure height. Three-dimensional shape of the sand deformation range in front of the MSC is dominated by the external structure height and the rotation center embedded depth. Based on the three-dimensional sand deformation behavior and limit equilibrium method, equations estimating the lateral bearing capacity of the MSC were proposed. The bearing capacities of MSCs obtained by using the proposed equations agree well with the test and numerical simulation results.

Importance of 3D analyses on static and seismic stability of jointed open-pit mine slopes

Most studies on open-pit mine stability have been performed in two-dimensional (2D) mode, which neglects the effect of the circular shape and thus the effect of third-direction boundary conditions. The aim of this work was to study the effect of the third dimension on static and dynamic stability analyses of pit slopes by comparing results from two- and three-dimensional (3D) numerical and limit equilibrium analyses. Geomechanical data from Choghart open-pit mine, located in the seismically active area of central Iran, were considered under a historical earthquake (M = 6.4). Kinematic analyses showed that two tectonic blocks of the mine – BL1 and BL2 – are susceptible to wedge and planar failures, respectively. The 2D and 3D static analyses showed that both blocks are stable, with higher safety factors (SFs) obtained using numerical 3D analyses. In the dynamic analyses, both 2D and 3D analyses showed wedge instability for BL1. However, for BL2, the 2D numerical analyses showed instability whereas the 3D numerical and pseudo-static analyses indicated block stability. The results revealed that the 3D SFs are generally 20–40% greater than those from 2D analyses. This can be explained by the consideration of the third-direction effect, verifying the importance of 3D analyses.

Limit equilibrium method-based 3D slope stability analysis for wide area considering influence of rainfall

We propose a method for evaluating the risks of slope failure induced by heavy rain over a wide area by combining infiltration analysis, surface flow analysis, and slope stability analysis based on three-dimensional limit equilibrium method. The influence of the resolution of terrain data is also examined. To determine rainfall-induced water transportation, we employ an infiltration analysis, using the Green-Ampt model, and a surface flow analysis, using the diffusion wave model. For the slope stability analysis, a three-dimensional arc-slip calculation applying the Hovland method is used. The infiltration depth is obtained from the results of the infiltration analysis, whereas the simulated data are used as input data for the slope stability analysis. A region in Kamaishi City, Iwate Prefecture, Japan, where slope failures were observed during typhoon Hagibis on October 12 and 13, 2019, is selected in this study as the target area and a series of analyses are performed. The topographical survey data by an Unmanned Aerial Vehicle (UAV) observed before and after the typhoon are used to identify the actual collapse locations and compare them with the results of the slope stability analysis. In addition, high-resolution topographic data of the target area using UAV data is created and differences in the factor of safety distribution with and without the UAV data for terrain data are compared and discussed. The obtained results revealed that the proposed method can roughly represent the actual slope failure, which is useful for evaluating rainfall-induced slope failure hazards. The results derived from utilizing detailed terrain data by UAV show the importance of using a high-resolution terrain model for evaluating the stability of microtopography, such as forest roads.

Determination of the Main Direction of a Sliding Body Based on a Three-Dimensional Finite-Element Limit-Equilibrium Method

Determination of the Main Direction of a Sliding Body Based on a Three-Dimensional Finite-Element Limit-Equilibrium Method

Three-dimensional limit equilibrium method for asymmetrical slope stability analysis

<p indent="0mm">A formula is proposed to calculate the DOS of 3D slopes based on the limit equilibrium theory. By combining the one-direction method with the proposed computational formula of DOS, a three-dimensional method for asymmetrical slope stability analysis based on one-direction force or/and moment equilibrium is proposed. The proposed method can compute both the factor of safety and the DOS of asymmetrical problems. As a result, the one-direction method’s potentially overestimated safety factors due to assumed DOS can be eliminated. Examples under static and pseudo-static forces are used to validate the proposed method’s logic and the algorithm’s astringency. The practical engineering examples further demonstrate the proposed method’s engineering applicability. The proposed method, with its simple principle and reliable results, can be widely used in slope design and landside treatment.

Composition analysis and distributed assumption GIS model of normal stress on the slope sliding surface

For the limit equilibrium method based on the assumption model of sliding surface normal stress, the more reasonable the assumed sliding surface normal stress model is, the higher the accuracy of the calculation results will be, which is of great significance to improve the theoretical calculation accuracy. Combined with the powerful spatial data analysis ability of Geographic Information Systems (GIS), the expression of the normal stress distribution function of the slip surface is deduced by establishing a GIS-based three-dimensional slope stability analysis model and limit equilibrium equations. By analyzing the composition of the normal stress distribution on the sliding surface, the composition of the normal stress on the sliding surface is obtained, and then the assumed model of the normal stress distribution on the sliding surface is constructed. Finally, the assumed GIS model of the sliding surface normal stress distribution is verified by calculating the proportion. The model overcomes the problem that the stability factor of the slope will cause large errors in the three-dimensional state, and provides a theoretical calculation basis for the establishment of a three-dimensional slope limit equilibrium method based on the assumption of normal stress on the slip surface in GIS.

Three-dimensional limit equilibrium slope stability analysis on real slope failures caused by heavy rain and earthquake

Three-dimensional limit equilibrium slope stability analysis on real slope failures caused by heavy rain and earthquake

An analytical model for face stability of tunnels traversing the fault fracture zone with high hydraulic pressure

The issue of tunnel face stability traversing the fault fracture zone with high hydraulic pressure has been addressed based on a new three-dimensional limit equilibrium model. First, the finite element numerical simulation is conducted to reveal the effects of the differences in permeability coefficient of strata on both sides of the geological interface on the distribution of seepage flow field nearby tunnel face. With this discovery, an existing universal approximate formula for hydraulic head nearby tunnel face is modified to accurately calculate the hydraulic head distributions under this scenario. Second, introducing the effect of geological interface, a new limit equilibrium model that consists of a trapezoid and a prism is proposed. The distributed loading exerted by the prism upon the trapezoid is deduced by considering the effects of seepage force and geological interface. Then, limit support pressure is derived according to the limit equilibrium state of the trapezoid. Finally, the comparison of the predicting results of the proposed limit equilibrium model with the results of the numerical simulations and the existing failure mechanism is performed, which indicates that the proposed trapezoid-prism model can well predict the tunnel face stability traversing the fault fracture zone with high hydraulic pressure.

Methodology for Resloping of Rock Slope Using 3D Models from UAV-CRP Technology

Assessing the stability of rock slopes is essential to ensuring the typical performance of adjacent transportation infrastructures but simulating the existing field topography and boundary conditions for stability analysis is challenging. This paper describes a case study in which highly weathered rock slopes adjacent to a railroad track in Texas were analyzed using close-range photogrammetry data obtained from an unmanned aerial vehicle with close-range photogrammetry (UAV-CRP). A highly weathered rock mass with low intact strength was considered as a single continuum that undergoes circular failure and was analyzed using Spencer’s two-dimensional (2D) and three-dimensional (3D) limit equilibrium method (LEM) analyses. A 3D critical slip surface was obtained to identify the critical sections on which to conduct the individual 2D stability analysis and obtain a safe resloping angle. These angles were further used to reslope the whole rock slopes and conduct a 3D analysis to arrive at a safe and economic slope angle for each side of the rock-cut. The realistic geometrical slopes developed from the aerial imagery were used to develop a framework for comprehensively analyzing the stability of a rock slope undergoing circular failure.

The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability

This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop’s average skeleton stress combined with the Mohr–Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions.

Three-Dimensional Limit Equilibrium Solution of Minimum Support Pressure of Shield Tunnel Face in Sandy Cobble Stratum

The ground subsidence accident caused by the instability of shield tunnel face has been a major problem that puzzles urban subway construction in weak rock. Maintaining the stability of tunnel face is the key to ensure the safety of shield construction and reduce the environmental impact. In view of the shield with a diameter of 8600 mm in Chengdu metro line 18 through the sandy cobble stratum, it is more difficult to maintain the stability of the shield tunnel face than other strata. The characteristics of the sandy pebble stratum were taken into account firstly in this paper. The analytical equation was obtained by the limit equilibrium method. The optimization of the trapezoidal bottom has been improved based on the existing 3D trapezoidal wedge model. And the optimal solution of the ultimate support pressure was obtained. The influencing factors of support pressure are also analysed. When the tunnel diameter is fixed, the deeper the ground covering depth is, the greater the required limit support pressure becomes. But the ground covering depth has almost no effect on the ultimate support pressure even if the tunnel is deep. The limit support pressure is inversely proportional to the internal friction angle of the soil and is proportional to the diameter of the tunnel. Finally, theoretical limit support pressure can be also verified by the numerical simulation results and the field monitoring results. It provides a reference for the subsequent setting value of the soil warehouse pressure.

Evaluating slope stability with 3D limit equilibrium technique and its application to landfill in China

A new derivation of the three-dimensional (3D) limit equilibrium method for slope stability analyses is presented, which applies linear algebra operations to matrices to achieve a highly efficient algorithm while maintaining the rigorousness of the formulation. It satisfies six equilibrium conditions and includes all of the components of the intercolumnar forces. The generalized 3D Morgenstern-Price's (MP) assumption for the intercolumn forces is recast into incremental forms. The advantage is that the unknowns of the different physical meanings (i.e., factor of safety (FS) and the coefficients in the MP assumption) are determined by balancing the forces and moments independently. Along with the recasting correction coefficients, they are solved with the triple nested algorithm. The numerical instability that is related to the different orders of magnitude for the residuals is avoided. The varication examples show: (i) the insensitivity of the FS to the prescribed functions in the MP assumption, (ii) the reliability of the method to cope with a complicated slope geometry (simplified methods may provide a larger FS for certain cases), and (iii) the superior efficiency of the algorithm (requires several seconds to converge). This study proposes a practical way to track the irregular 3D tension cracking by repeating the analysis and excluding the columns with the negative normal forces at the bottom. This formulation is applied to a valley landfill slope in China. In comparison to the two-dimensional analysis, there are more reasonable/cost-effective measures to increase the system stability through 3D analyses for several conditions (e.g., seismic loading).

Landslide monitoring and runout hazard assessment by integrating multi-source remote sensing and numerical models: an application to the Gold Basin landslide complex, northern Washington

The landslide complex at Gold Basin, Washington, has been drawing considerable attention after a catastrophic runout of the nearby landslide at Oso, Washington, in 2014. To evaluate potential threats of the Gold Basin landslide to the campground down the slope, remote sensing and numerical modeling were integrated to monitor recent landslide activity and simulate hypothetical runout scenarios. Bare-earth LiDAR DEM (digital elevation model) differencing, InSAR (Interferometric Synthetic Aperture Radar), and offset tracking of SAR images reveal that localized collapses at the headscarps have been the primary type of landslide activity at Gold Basin from 2005 to 2019, and currently no signs indicative of movement of a large centralized block or a deep-seated main body were detected. The maximum horizontal deformation rate is 5 m/year occurring primarily from headscarp recession of the middle lobe, and the annual landsliding volume of the whole landslide complex averages 1.03 × 105 m3. From three-dimensional limit equilibrium analysis of generalized terrace structures, the maximum landslide volume is estimated as 2.0 × 106 m3. Simulations of hypothetical runout scenarios were carried out using the depth-averaged two-phase model D-claw with above-obtained landslide geometry constraints. The simulation results demonstrate that debris flows with volume less than 105 m3 only pose limited threats to the campground, while volumes over 106 m3 could cause severe damages. Consequently, the estimated maximum landslide volume of 2.0 × 106 m3 suggests a potential risk to the campground nearby. Adaption of our methodology could prove useful for evaluating other similar landslides globally for hazards prevention and mitigation.

Preface

The previous 2019 International Conference on Civil, Architecture and Urban Engineering (ICCAUE 2019) was successfully taken place on October 18-20, 2019 in Chongqing, China. It was a great pleasure to welcome all the participants from different countries to the 2020 2nd International Conference on Civil, Architecture and Urban Engineering (ICCAUE 2020) in Xi’an China during August 14–16. This three-day conference was hosted by Tianjin Port Engineering Institute Co., Ltd. of CCCC First Harbor Engineering Co., Ltd., presented by AEIC Academic Exchange Information Center. The conference is an international conference for the presentation of technological advances and research results in the fields of civil, architecture and urban engineering. The conference brings together over 90 leading researchers, engineers and scientists in the domain of interest from around the world.The conference model was divided into two sessions, including oral presentations and keynote speeches. In the first part, some scholars, whose submissions were selected as the excellent papers, were given 15 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-45 minutes to hold their speeches.In this conference, we are greatly honored to have invited Prof. Aimin Liu from Tianjin Port Engineering Institute Co., Ltd. of CCCC First Harbor Engineering Co., Ltd., China to serve as our Conference Chairmen. During the conference, we were pleased to invite four distinguished experts to present their insightful speeches. The first keynote speaker, Prof. Wai Yuen SZETO, The University of Hong Kong, China, held a speech on Taxi Service Area Design. This study proposed a nonlinear mixed integer programming model to determine the service areas. The objective is to maximize social welfare. Prof. Yanlong Li from Xi’an University of Technology, China, talked about Research on the deterioration mechanism of concrete with initial damage under different load modes. His speech presented some current work on the relationship between internal damage and nonlinear creep of concrete, revealed the expansion law of crack morphology under the stress mode of hydraulic concrete. A. Prof. Zhuangzhuang Liu, Chang’an University, China, shared a speech on his specialty related to Research on snow self-melting asphalt pavement technology based on targeted heat conduction. This research designed a kind of high thermal conductivity asphalt concrete, studied the influence of key materials such as heating element, heat conductor and insulation on the heating effect of concrete, and verified the influence factors of environmental temperature, the amount of snow and working time on snow melting effect. As the last keynote speaker, Prof. Chenghua Wang from Tianjin University, China, made an insightful speech on A Three-dimensional Limit Equilibrium Method for Analysing the Basal Upheaval Stability of Deep Slender Foundation Pits. The conference provided a forum for discussing Civil, Architecture and Urban Engineering and in particular for promoting the interchange of novel ideas and the presentations of the latest developments in this field. This conference will also provide an ideal environment to develop new collaborations and meet experts on the fundamentals, applications, and products of the mentioned fields.We are glad to share with you that we received lots of submissions from the conference and we selected a bunch of high-quality papers and compiled them into the proceedings after rigorously reviewed them. These papers feature following topics but are not limited to: Civil Engineering, Architecture, Urban Engineering, Urban traffic management and other related topics. All the papers have been through rigorous review and process to meet the requirements of International publication standard.We are really grateful to the International/National advisory committee, keynote speakers, session chairs, organising committee members, student volunteers and administrative assistance of the management section of University, including accounts section, digital media and publication house. Also, we are thankful to all the authors for contributing a large number of papers in the conference, because of which the conference became a story of success. It was the quality of their presentations and their passion to communicate with the other participants that really make this conference series a great success.The Organizing Committee of ICCAUE 2020Committee member Chairs, Organizing Committees, Academic Committees are available in the pdf.

A three-dimensional limit equilibrium method for analysing the basal upheaval stability of deep slender foundation pits

Deep slender foundation pits, which are of small plane dimensions and deep retaining structures, have been increasingly used in engineering practice. Spatial effects of this type of foundation pits are obvious, but the existing stability analysis methods are not suitable for such deep foundation pits. Therefore, three-dimensional basal upheaval stability analysis methods considering the spatial effect are badly needed. On basis of former tests and numerical solutions, a new model of upheaval failure for deep slender foundation pits was suggested by application of the limit equilibrium technique for entire foundation pits, considering the influences of spatial effects of the retaining structures. A global factor of safety against upheaval instability was defined and the applicability of the method was demonstrated with some parametric analyses.

Evaluation of rock slopes susceptible to circular failures using logistic and multiple regression models

The analysis of stability of slopes is a classical problem for geotechnical engineers. In practice, many methods are available for the desired purpose, from basic kinematic analysis to two- and three-dimensional limit equilibrium analyses and numerical modeling with various user-friendly softwares. However, additional techniques are also required to provide knowledge necessary for decision-making. In this research, a reliable dataset provided by Sah et al. (1994) was used to analyze the stability evaluation of rock slopes subjected to circular failures. For this purpose, using Slide 2018 program, 44 separate limit equilibrium slope models were built for each case given in the original work. The provided material properties and slope geometries in heavily fractured and/or very weak or highly weathered rock masses were considered during the model building stage. It was found that Slide 2018 program generated dissimilar safety factors compared to those given by Sah et al. (1994) for the investigated slope cases. Binary logistic and multiple linear regression techniques were implemented in the study to promote alternative approaches for the prediction of the stability condition and safety factor (SF) of slopes excavated in heavily fractured/highly weathered rock masses. The condition of slopes (stable or failed) was predicted by binary logistic regression model with 90.9% accuracy. The SF of the slopes was estimated by a multiple linear regression model with 95.6% accuracy. It was concluded that both statistical techniques could be sufficiently used as alternative approaches to predict the stability condition and SF of rock slopes prone to circular (rotational) failures.

A Strength Design Method of Cemented Backfill with a High Aspect Ratio

To calculate the required strength of a cemented backfill with high aspect ratio, the confirmation of lateral pressure is fundamental and needs to be determined first. As for the backfill with a high aspect ratio of height to length, the shape of the slip surface is not straight when in the active state due to the limited space, which is different from the general backfill. For this reason, a formulation of the slip surface with a curved shape and a lateral pressure calculation method based on this curved slip surface were proposed. The proposed equation of the slip surface is affected by the geometry parameters of the backfill, internal friction angle of the backfill, and the friction angle of the backfill‐rock interface. Then, by the combination of the minor principal stress trajectory method and the horizontal slice method, an ordinary differential equation of stresses was established and then solved numerically. Finally, the method based on Mitchell’s three‐dimensional limit equilibrium model was used to calculate the required strength of the cemented backfill. The calculated results were compared with previous studies and validated with numerical models. The results showed good consistency for the backfills with high aspect ratios.

Three-dimensional limit equilibrium method based on a TIN sliding surface

The three-dimensional limit equilibrium method (3D LEM) is an important approach for analysing slope stability, and the rationality of simulations for sliding surfaces directly affects the factor of safety (FoS) accuracy. Typically, the grid model containing grid elements with fixed size and uniform distribution in a digital elevation model (DEM) is used to simulate sliding surfaces. However, it is difficult to accurately express the real sliding surface shape unless a sufficient number of grid elements are used. Moreover, the four vertexes in each grid with different elevations are assumed to be located in the same plane, which may result in incorrect slope parameters and degraded FoS accuracy. To overcome these shortcomings, the triangulated irregular network (TIN) model is adopted to construct sliding surfaces, making full use of the flexibility and accuracy of triangular elements in describing surfaces and the uniqueness of the plane determined by three vertexes. A method to generalize and simplify TIN sliding surfaces is proposed based on Visualization Toolkit (VTK) open source library modules. Furthermore, combined with the Hovland method, a 3D LEM model based on a TIN is presented, and the corresponding calculation module is written and compiled in Python. To compare the FoS precision and computational efficiency, several classic examples with ellipsoidal and planar sliding surfaces are used to analyse the slope stability. The results show that, under the condition of obtaining nearly the same FoS, the number of triangles needed can be ordered from lowest to highest as follows: the simplified TIN sliding surface, unsimplified TIN, and grid model. In addition, the computation time required for the grid model is many times higher than that of the TIN sliding surface. Therefore, compared with the grid model, the TIN sliding surface adopted in the 3D LEM can effectively improve the accuracy and efficiency of FoS calculations.

Two- and three-dimensional slope stability evaluation in a residential area: Denizkonak landslides in Cide (Kastamonu, NW Turkey)

In this study, it was aimed at evaluating the slope stability conditions in a residential area exposed to two landslides in the past by using two- and three-dimensional limit equilibrium analyses. Two separate, but interdependent, landslides were observed in the investigated area. In 1992 and 1994, two landslides occurred in the region after heavy precipitation and caused damages on the houses and infrastructures. An extensive field work was performed to obtain input parameters for the analyses. In addition, an unmanned aerial vehicle was flown to obtain a three-dimensional view of the landslide area for better understanding of the past failures. The landslides occurred in a flysch-type material representing complex geological characteristics. Hoek–Brown failure criterion and Geological Strength Index were chosen for the strength and visual definition of the geological unit. Since the landslide triggering factor was precipitation, the analyses were focused on the water conditions causing the failure. Sensitivity and back-analyses were performed to obtain the conditions of failure. It was revealed that a high pore pressure ratio was needed to trigger the landslides. However, the second landslide was failed with a lower pore water pressure and the current topography was determined to be on the edge of failure with a slight increase in the pore pressure ratio. In other words, the study area was still found to be prone to possible landslides in the future.

Three-dimensional stability analysis of seismically induced landslides using the displacement-based rigorous limit equilibrium method

Previously, the stability analysis of seismically induced landslides was investigated by the factor of safety of the entire sliding body, which provided no information on the displacements of the analyzed seismically induced landslides. The landslides are assessed to be dangerous when the minimum value of the factor of safety (Fs) is less than a critical value. However, unlike the landslides subjected to static loads, the dynamic safety factors of seismically induced landslides vary with time. The minimum value of the dynamic safety factors being less than the critical value does not necessarily imply failure of the seismically induced landslides. In this paper, the three-dimensional displacement-based rigorous limit equilibrium method is proposed to study the displacements of seismically induced landslides. The relationship between the shear stresses acting on the base of the columns and the shear displacements is established based on the hyperbolic soil model. By introducing the strength reduction technique, the relationship between the reduction factor (RF) and the accumulated vertical displacement can be obtained. According to the definition of the strength reduction method, the safety factors of seismically induced landslides are determined, which do not vary with time. Then, the landslides can be assessed to be dangerous when the minimum value of Fs is less than a critical value.