Associate Professor Jinsong Huang

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. This article presents a case study of the stability of the south anchorage of Taizhou Yangtze River Bridge in China. The gravity anchorage was embedded in soil and designed according to the current code of China. The code-based stability assessment is based on two-dimensional (2D) analyses under the assumption of plane strain conditions. Two typical failure modes of sliding and overturning are considered separately. The 2D plane strain model assumes the size of a structure in one dimension is significantly larger than the sizes in the other two dimensions. It is, thus, unsuitable for gravity anchorage because its sizes are similar in all three dimensions. Additionally, the effect of surrounding soil is ignored apart from the base friction in the anti-sliding stability assumption leading to the conservative design. Therefore, a three-dimensional model is more appropriate. Three-dimensional finite element model combined with strength reduction method is used to analyse the stability of anchorage. Reduced-scale model tests are used to calibrate the numerical model. The results show that the code-based design is indeed too conservative. The effects of stiffness and strength of the surrounding soil on the stability of anchorage are investigated through parametric studies to facilitate the economical design of gravity anchorage.

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. The environmental factors of landslide susceptibility are generally uncorrelated or non-linearly correlated, resulting in the limited prediction performances of conventional machine learning methods for landslide susceptibility prediction (LSP). Deep learning methods can exploit low-level features and high-level representations of information from environmental factors. In this paper, a novel deep learning¿based algorithm, the fully connected spare autoencoder (FC-SAE), is proposed for LSP. The FC-SAE consists of four steps: raw feature dropout in input layers, a sparse feature encoder in hidden layers, sparse feature extraction in output layers, and classification and prediction. The Sinan County of Guizhou Province in China, with a total of 23,195 landslide grid cells (306 recorded landslides) and 23,195 randomly selected non-landslide grid cells, was used as study case. The frequency ratio values of 27 environmental factors were taken as the input variables of FC-SAE. All 46,390 landslide and non-landslide grid cells were randomly divided into a training dataset (70%) and a test dataset (30%). By analyzing real landslide/non-landslide data, the performances of the FC-SAE and two other conventional machine learning methods, support vector machine (SVM) and back-propagation neural network (BPNN), were compared. The results show that the prediction rate and total accuracies of the FC-SAE are 0.854 and 85.2% which are higher than those of the SVM-only (0.827 and 81.56%) and BPNN (0.819 and 80.86%), respectively. In conclusion, the asymmetric and unsupervised FC-SAE can extract optimal non-linear features from environmental factors successfully, outperforms some conventional machine learning methods, and is promising for LSP.

© 2017 Among the machine learning models used for landslide susceptibility indexes calculation, the support vector machine (SVM) is commonly used; however, SVM is time-consuming. In addition, the non-landslide grid cells are selected randomly and/or subjectively, which may result in unreasonable training and validating data for the machine learning models. This study proposes the self-organizing-map (SOM) network-based extreme learning machine (ELM) model to calculate the landslide susceptibility indexes. Wanzhou district in Three Gorges Reservoir Area is selected as the study area. Nine environmental factors are chosen as input variables and 639 investigated landslides are used as recorded landslides. First, an initial landslide susceptibility map is produced using the SOM network, and the reasonable non-landslide grid cells are subsequently selected from the very low susceptible area. Next, the final landslide susceptibility map is produced using the ELM model based on the recorded landslides and reasonable non-landslide grid cells. The single ELM model which selects the non-landslide grid cells randomly, and the SOM network-based SVM model are used for comparisons. It is concluded that the SOM-ELM model possesses higher success and prediction rates than the single ELM and SOM-SVM models, and the ELM has a considerably higher prediction efficiency than the SVM.

© 2016 Elsevier Ltd How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the ¿max¿ and ¿min¿ functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.

© 2017 The Author(s). It is important to monitor the displacement time series and to explore the failure mechanism of reservoir landslide for early warning. Traditionally, it is a challenge to monitor the landslide displacements real-timely and automatically. Globe Position System (GPS) is considered as the best real-time monitoring technology, however, the accuracies of the landslide displacements monitored by GPS are not assessed effectively. A web-based GPS system is developed to monitor the landslide displacements real-timely and automatically in this study. And the discrete wavelet transform (DWT) is proposed to assess the accuracy of the GPS monitoring displacements. Wangmiao landslide in Three Gorges Reservoir area in China is used as case study. The results show that the web-based GPS system has advantages of high precision, real-time, remote control and automation for landslide monitoring; the Root Mean Square Errors of the monitoring landslide displacements are less than 5 mm. Meanwhile, the results also show that a rapidly falling reservoir water level can trigger the reactivation of Wangmiao landslide. Heavy rainfall is also an important factor, but not a crucial component.

© 2017 Elsevier Ltd Spudcan foundations are often pushed into a spatially varying non-homogeneous seabed to provide bearing capacity for a mobile jack-up platform. The natural variability of soil properties coupled with the complexity of loading conditions make determining the bearing capacity of spudcan foundations a challenging problem. A random finite element method is established to investigate the bearing capacity of a spudcan foundation embedded in a spatially varying clayey seabed when subjected to vertical, horizontal and moment loadings. A criterion is proposed for determining the characteristic value of the shear strength for the random seabed. Results indicate that the spatial variability in the clayey seabed significantly reduces the bearing capacity of a spudcan foundation. This reduction is more significant in the vertical bearing capacity than in the horizontal and moment bearing capacities. The mean bearing capacity is smaller for the clay with larger coefficient of variation of undrained shear strength. A characteristic value of mean minus a standard deviation of the undrained shear strength is capable to ensure the probability of failure is not greater than 5%. This study provide an evaluation method for the spatial variability effect of a clayey seabed, paving the way for a cost-effective design of spudcan foundations.

© 2015 Elsevier Ltd. Pile load tests are used to refine designs and for quality assurance. They can also be used to verify the reliability of piles and pile groups. Stochastic methods have previously been developed to verify the reliability of single piles. A general stochastic method to verify the reliability of pile groups is developed in this paper. The method can be used to assess the reliability of groups where pile tests have been conducted to the ultimate capacity, to below the ultimate capacity but exceeding specified capacity, and where pile tests fail to achieve the specified capacity. In the latter case, the method allows decisions to be made as to whether the reliability of the entire pile group is satisfactory or whether additional piles need to be installed.

© 2015 Taylor & Francis. The limit analysis and the finite element method are powerful tools for analysing the bearing capacity of foundations. Previous research mainly focused on the foundations in uniform soils. In realistic conditions, soil properties are always varying spatially due to complex physical, chemical, and biological process in earth evolution. This paper investigates the bearing capacity and failure mechanism of footings buried at various depths in clays with spatially variable distribution of undrained shear strength using the lower bound limit analysis, the upper bound limit analysis, and the finite element analysis. Results show that the bearing capacity increases with increasing buried depths in spatially random soils, which is the same as in the uniform soils. The bearing capacity factors calculated using the finite element method, the lower bound limit analysis, and the upper bound limit analysis for a footing in spatially varied soils are all smaller than the corresponding values in uniform soils. The majority of the bearing capacity factors obtained from the finite element method is bounded by those obtained from the lower bound and the upper bound limit analysis. The shear planes show a clearly unsymmetrical manner in spatially varied soils using the three methods, which is different from the symmetrical shear plane in uniform soils.

© 2015, National Research Council of Canada, All Rights Reserved. After a geotechnical design has been developed, it is common to monitor performance during construction using the observational method by Peck (published in 1969). The observational method is a process where data are collected and geotechnical models updated, allowing timely decisions to be made with respect to risk and opportunity by asset owners or contractors. The observational method is similar to the mathematical formulation for Bayesian updating of material parameters based on measurements. A proof of concept study has been performed to assess the potential for Bayesian updating to be combined with the observational method to allow timely and accurate decision-making during construction of embankments on soft soils. The method was able to converge to an accurate solution prior to 50% consolidation assuming small measurement errors. It is also demonstrated that confidence in the predicted settlement is relatively low at the prior ¿design¿ stage and rapidly increases with three or four measurements spaced over time during the posterior ¿construction¿ phase.

© 2015 Elsevier Ltd. The mechanical properties of dry soil mix (DSM) columns can be highly variable. Variability can be accounted for in the construction specification for deterministic design and directly in reliability based design. Design methods and specifications to date adopt simplifications that do not take the variability of the columns fully into account. This paper uses both simple and advanced probabilistic methods to assess the performance/failure and system redundancy of dry soil mix columns. Reliability-based design methods and examples are given for the design of column strength and the adjustment of the column spacing to achieve a target probability of unacceptable performance or failure. An acceptance criteria chart is developed. The pull-out resistance tests on the DSM columns constructed for the Ballina Bypass motorway construction project in NSW Australia are compared to the chart to provide guidance with respect to acceptance criteria required to achieve the desired performance.

Rainfall induced landslides vary in depth and the deeper the landslide, the greater the damage it causes. This paper investigates, quantitatively, the risk of rainfall induced landslides by assessing the consequence of each failure. The influence of the spatial variability of the saturated hydraulic conductivity and the nature of triggering mechanisms on the risk of rainfall-induced landslides (for an infinite slope) are studied. It is shown that a critical spatial correlation length exists at which the risk is a maximum and the risk is higher when the failure occurs due to a generation of positive pore water pressure. © 2014 Elsevier B.V.

In the study of landslides, it is generally assumed that an impermeable boundary exists at a certain depth and failure occurs at this boundary. In reality this is not always the case and failures can occur at any depth. This paper aims to study the effect of boundary conditions on landslides, using a series of seepage and stability analyses performed over a range of rainfall intensities, and for different failure mechanisms, by studying the failure time and depths corresponding to fully drained, partially drained, and impermeable boundaries. It is shown that these conditions can significantly affect the occurrence and depth of rainfall-induced landslides. © 2014 Elsevier Ltd.

The observational method is one of the most successful processes in geotechnical engineering. Performance monitoring data are the most reliable information that engineers can use to predict future performance of geotechnical projects. This paper presents two examples where Bayesian statistical methods can be used for the prediction of future performance. The first example is to update the capacity of piles using load test results. The second example is to update embankment settlement predictions when field settlement monitoring data are available.

This paper investigates the soil properties, stratigraphy and spatial variability of the soils at the National Field Test Facility in Ballina based on extensive CPTU tests. The soil profile in this site consists of an alluvial crust over a relatively weaker layer of clay and underlain with a layer of sand and Pleistocene age stiff clay. The measured cone penetration resistance, sleeve friction and pore pressure for 26 CPTUs are presented along with the deployment of the CPTUs. The spatial variability in both vertical and horizontal direction of each layer of soils is explored based on the CPTU tests. An exponential autocorrelation function is found to best fit the autocorrelation coefficients. The scale of fluctuation in the vertical direction is 0.04 m in the alluvial crust layer, which is much smaller than that in the underlying clay layer, 0.15 m. The reason is that the clay was deposited under lower energy conditions compared to the more granular crust layers. The horizontal scale of fluctuation is 9.21 m in the alluvial crust layer and 4.92 m in the clay layer.

© 2003, Editorial Department of Engineering Journal of Wuhan University. All right reserved. On the basis of new normative principles, criterions and methods such as Design specification for concrete gravity dams and Specifications for seismic design of hydraulic structures, we calculated the normal use ultimate strength and the carrying capacity ultimate strength of Dachaoshan dam according to the finite element method. The result indicates that the gravity dam is safe and credible; the dam's structure totally reaches the reliability level stated by criterions.

© 2003, Editorial Department of Engineering Journal of Wuhan University. All right reserved. Two methods for estimating the ultimate bearing capacity of gravity dam are studied. The first method is to see whether or not the yield area across the dam. The second method called energy method is to define the ultimate state of the dam. Aiming at a real project, the example is given. It is found that the second method usually gets the lower result.

The paper presents a finite element model for strength analyses of a rotational composite shell under axial compression and internal pressure. The characteristics of stress distribution, stress locations and loads of failure are determined according to the model. The model is also developed to calculate the stability of the shell under axial compression, external pressure and combination of the both. Experiments are completed for studying the strength of the shell under axial compression and internal pressure and the stability of the shell under the combination of axial compression and external pressure.

©, 1998, Journal of Huazhong University of Science and Technology. All right reserved A stability calculation method of laminated-composite dome structure is presented based on the modified-equivalent cylindrical shell model. The method is used to calculated the stabili ty of missile's dome under axial compression, external pressure and their combination respectively, and some experiments are completed for studying the stability of the dome under combined load. Finally, the relations between the dome's load of failure with characteristic size and laminated form are analyzed and discussed.

Since the charts ofTaylor, it has beenwell knownthat the location of the critical failure mechanism in a homogeneous undrained clay slope goes either deep (tangent to a firm base) or shallow (through the toe) depending on whether the slope angle is, respectively, less than or greater than about 53°. When slopes are made up of variable soils however, these expectations no longer hold true for all cases. In this paper, the influence of random soil strength and slope angle on the location of the critical failure mechanism and probability of failure is examined using the Random Finite Element Method (RFEM). It is found following Monte-Carlo simulation, that there exists a critical value of slope angle above which it would be unconservative to assume high spatial correlation length and below which it would be conservative to assume high spatial correlation length. For ß>48°, both correlation length and slope angle have no influence on the proportion of toe failures. For slope angle lying between 20° and 40°, slopes that have higher correlation length give lower proportion of toe failures. Research into the critical mechanism location forms part of a broader study of slope failure risk, in which the consequences of failure are assumed to be more serious in a deep failure, because a greater volume of soil is affected. © 2015 Taylor & Francis Group, London.

Bearing capacity and failure mechanism of a buried footing in uniformsoils have been simulated using limit analysis and finite element analysis in the past decades. In realistic conditions, soil properties always vary spatially. This dramatically affects the failure mechanism of a footing and, in turn, its bearing capacity. This paper illustrates an investigation into the failure mechanism and bearing capacity of a vertically and centrally loaded footing embedded in spatially variable clayey soils using random lower bound limit analysis, random upper bound limit analysis and random finite element analysis. The footing was embedded to 4 times its width. Monte Carlo simulation was performed for 400 realizations of random fields of undrained shear strength. The majority of the bearing capacity factors obtained from the finite element method is bounded by those obtained from the lower bound limit analysis and the upper bound limit analysis, but more close to the upper bound results. A full-flow failure mechanism is observed for the deeply embedded footing in spatially variable soil. The shear path of the footing shows an unsymmetrical pattern, which results from the spatially variable and unsymmetrical random field of soil shear strength. © 2015 Taylor & Francis Group, London.

Rainfall induced landslides can vary in depth and deeper the landslide, greater is the damage it causes. This paper investigates, quantitatively, the risk of rainfall induced landslides by assessing the consequence of each failure. The influence of the spatial variability of the saturated hydraulic conductivity on the risk of landslides is studied. It is shown that a critical spatial correlation length exists at which the risk is a maximum. © 2015 Taylor & Francis Group, London.

In deep drilling operation, borehole collapse due to insufficient drilling fluid pressure and borehole fracturing as a result of excessive drilling fluid pressure are two major modes of borehole failure. The latter may result in severe loss of drilling fluid into the formation, resulting in potential well control issues with influx of high pressure fluid or gas from adjacent formation layers. To prevent drilling fluid loss, the fluid pressure must not exceed an upper limit, otherwise the borehole will fail in tension or fracture. However, if the fluid pressure is too low, the borehole may collapse or fail in compression. Drilling fluid pressure window is therefore typically set by the upper limit of tensile failure and the lower limit of compressive failure. If the stress state and rock strength require a lower limit which is close to the upper limit, then the drilling fluid pressure design needs to stay within a very narrow window and consequently the feasibility of drilling may be questioned. Based on rigorous mechanics principles, this paper shows that it is possible to experience shear failure due to increasing drilling fluid pressure even before it reaches the upper limit of tensile failure. This may mean a more restricting drilling fluid pressure window in drilling weaker rocks. Implications of near wellbore shear failure are also briefly discussed in the context of water injection design which relies on injection at high pressure. © 2015 Taylor & Francis Group, London.

Copyright 2014, International Petroleum Technology Conference The drilling induced tensile fractures can be observed from borehole image logs but they must be differentiated from natural fractures. This paper focuses on the understanding of hydraulically or artificially induced tensile fractures while drilling. We present an inversion method using rigorous principles of mechanics, to determine the in-situ formation stress state from observed induced tensile fractures. Contrary to common practices where only vertical or near vertical wells can be analysed, the present method is applicable to wellbores of all orientations. For a geological rock formation and area where the in-situ stress regime can be assumed to be similar, all the relevant borehole image logs can be included to provide information to yield the most probable subsurface in-situ stress state. The proposed inversion method directly solves for the in-situ stress states given any single set of observed tensile fracture location and orientation. It provides not only an estimate for the minimum horizontal stress magnitude and direction, but also the maximum horizontal stress magnitude which is usually very difficult to pin down. The resultant equations are non-linear and a simple numerical scheme is adopted for the solution. Although published data on borehole images of fractures with corresponding in-situ stress information are scarce, two observed field data from published papers are chosen for comparison.

The mechanical properties of natural materials such as rocks and soils vary spatially. This randomness is usually modelled by random field theory so that the material properties can be specified at each point in space. When these point-wise material properties are mapped onto a finite element mesh, discretization errors are inevitable. In this study, the discretization errors are studied and suggestions for element sizes in relation with spatial correlation lengths are given. © (2014) Trans Tech Publications, Switzerland.

The homogenized stiffness of geomaterials that are highly variable at the micro-scale has long been of interest to geotechnical engineers. The purpose of this study is to investigate the influence of porosity and void size on the homogenized or effective properties of geomaterials. A Random Finite Element Method (RFEM) has been developed enabling the generation of spatially random voids of given porosity and size within a block of geomaterial. Following Monte-Carlo simulations, the mean and standard deviation of the effective property can be estimated leading to a probabilistic interpretation involving deformations. The probabilistic approach represents a rational methodology for guiding engineers in the risk management process. The influence of block size and the Representative Volume Elements (RVE) are discussed, in addition to the influence of anisotropy on the effective Young's modulus. © 2014 Taylor & Francis Group, London.

Analytical probabilistic analysis and Monte Carlo simulation based on elasto-plastic Finite Element Method (FEM) on dry soil mix columns are presented. It is shown that analytical method is over conservative because it ignores the supports from adjacent columns. Probabilistic FEM analysis can provide more accurate predictions, and thus lead to more economic designs. Probabilistic FEM analyses show that the effects of adjacent columns can be destructive when applied load is close to the strength. The reliability of the system of columns is analyzed by setting residual strength to zero. Results show that close spacing has more safety margin than loose spacing. © 2014 Taylor & Francis Group, London.

Program PES (Probabilistic Engineered Slopes) provides a repeatable methodology allowing the user to perform a slope stability analysis on a one-sided and two-sided sloping structure using a deterministic or probabilistic approach. Program PES, in contrast with other deterministic or probabilistic classical slope stability methodologies, is cable of seeking out the critical failure surface without assigning a pre-defined failure surface geometry. The probabilistic approach of program PES applies the Random Finite Element Method (RFEM) by Griffiths and Fenton (1993) taking into account the soil spatial variability and allowing the use of different random fields to characterize the spatial variation of any material type. The methodology is compared against the probabilistic approach proposed by the program SLOPE/W version 7.14 (Geostudio Group, 2007), and demonstrates its potential for predicting probability of failure (pf) in non-homogeneous soil structures characterized by phreatic conditions and potential post-earthquake liquefiable conditions. The pf results obtained by program PES have proved that underestimating the influence that the soil material variability has on the computation of pf will lead to lower results of probability and underestimate of the risk of slope instability. Program PES capabilities could be used by the engineering practice to prioritize intervention activities within a risk context. © 2011 American Society of Civil Engineers.

The paper describes probabilistic analyses performed as part of a large expansion to an existing cement manufacturing plant. A raft supported by drilled shafts was proposed for the project, but during installation, significant slurry and concrete loss began to occur indicating numerous voids existed in what was previously considered competent limestone bedrock. Since the possibility of voids, especially at the shaft tip, could serious reduce the shaft capacity, a probabilistic Monte Carlo 3D finite element simulation was proposed for the most heavily loaded raft foundation. The purpose of the simulation was to determine the probability of adverse performance, giving guidance as to whether any remedial measures (e.g., additional structural elements or thickened raft) might be required. © 2011 ASCE.

Reliability tools have been applied to slope stability analysis more than any other geotechnical application on account of the readily understood concept of "probability of failure" as an alternative or complement to the traditional "factor of safety". Probabilistic slope stability methods in the literature are reviewed. Particular attention is focused on the ability of the methods to correctly model spatially varying soil properties. A benchmark slope is reanalyzed and conclusions reached about their suitability for meaningful and conservative prediction of slope reliability. © 2010 ASCE.

The computer program Probabilistic Engineered Slopes (PES), coded in FORTRAN.95, provides a repeatable methodology, which allows the user to perform a slope stability analysis on a one- and two-sided sloping structure, using a deterministic or probabilistic approach. The program PES, in contrast with other deterministic or probabilistic classical slope stability methodologies, is capable of seeking out the critical failure surface without assigning a predefined failure surface geometry. The probabilistic approach of PES applies the Random Finite Element Method (RFEM) by Griffiths and Fenton (1993) [1], taking into account the soil spatial variability and allowing the use of different random fields to characterize the spatial variation of any material type. The methodology is compared against the probabilistic approach proposed with the program SLOPE/W, version 7.14 (Geostudio Group, 2007) [2], and demonstrates its potential for predicting probability of failure (pf) in nonhomogeneous soil structures for given phreatic conditions and potential postearthquake liquefiable conditions. The pf results obtained by program PES have proved that underestimating the influence that the soil material variability has on the computation of pf will lead to unconservative results of probability and underestimate of the risk of slope instability. The program PES has capabilities that could be used by the engineering practice to prioritize intervention activities within a risk context, test the stability conditions of dams during modification phases, and help estimate the probability of failure in cases involving postearthquake liquefaction.

The computer program Probabilistic Engineered Slopes (PES), coded in FORTRAN.95, provides a repeatable methodology, which allows the user to perform a slope stability analysis on a one- and two-sided sloping structure, using a deterministic or probabilistic approach. The program PES, in contrast with other deterministic or probabilistic classical slope stability methodologies, is capable of seeking out the critical failure surface without assigning a predefined failure surface geometry. The probabilistic approach of PES applies the Random Finite Element Method (RFEM) by Griffiths and Fenton (1993) [1], taking into account the soil spatial variability and allowing the use of different random fields to characterize the spatial variation of any material type. The methodology is compared against the probabilistic approach proposed with the program SLOPE/W, version 7.14 (Geostudio Group, 2007) [2], and demonstrates its potential for predicting probability of failure (pf) in nonhomogeneous soil structures for given phreatic conditions and potential postearthquake liquefiable conditions. The pfresults obtained by program PES have proved that underestimating the influence that the soil material variability has on the computation of pfwill lead to unconservative results of probability and underestimate of the risk of slope instability. The program PES has capabilities that could be used by the engineering practice to prioritize intervention activities within a risk context, test the stability conditions of dams during modification phases, and help estimate the probability of failure in cases involving postearthquake liquefaction.

The paper investigates the probability of failure of 2-d and 3-d slopes using the Random Finite Element Method (RFEM). RFEM combines elastoplasticity with random field theory in a Monte-Carlo framework. It is found that 2-d probabilistic analysis, by implicitly assuming perfect spatial correlation in the third direction, may underestimate the probability of failure of slopes. © 2009 IOS Press.

The influence of a spatially random coefficient of consolidation on one-dimensional uncoupled consolidation has been studied using the Random Finite Element Method. The results of parametric studies are presented, which describe the effect of the standard deviation and correlation length of the coefficient of consolidation on output statistics relating to the overall "effective" coefficient of consolidation. Three "effective" coefficient of consolidation are considered, namely harmonic mean, the log time method and the root time method. Copyright ASCE 2008.

The study investigates the role of spatially random soil on the stability of infinite slopes with application to landslides and other geohazards. The influence of the shear strength mean, standard deviation and spatial correlation length on the probability of failure is thoroughly investigated through parametric studies. The results show that the traditional "first order second moment" approach to this problem is inherently unconservative, due to its inability to allow the failure mechanism to "seek out" the critical depth below ground surface, which is frequently not at the base of the soil layer. Copyright ASCE 2008.

The paper presents probabilistic studies that demonstrate the influence of spatially random soil properties on the stability of shallow landslides using random fields Results indicate that traditional "first order" methods are inherently unconservative when applied to limit analysis problems unless they allow the failure mechanism to "seek out" the most critical location.