Random Finite Element Method Research Articles

Effect of pile inclination on the lateral deformation behaviour of pipe piles in calcareous sand

The lateral deformation behaviour of inclined piles in calcareous sand is investigated with model testing and numerical analysis. A model pile is instrumented with quasi-distributed strain sensors and installed in calcareous sand with various inclination angles. The lateral deformation, bending moment and shear force of the pile are analysed by investigating the effect of the inclination angle and embedded depth. The experimental results of piles with inclination angles of −30°, 0° and 30° are analysed. A random finite element method (RFEM) is established to investigate the effect of the pile inclination. A single exponential function is used to characterize the spatial autocorrelation of soil parameters. A random field is obtained by the Cholesky method. The RFEM is verified with experimental results and used to further analyse the lateral deformation behaviour. The results indicate that both of the orthogonal maximum influence distances from the pile centre have a linear relationship with the pile inclination. A linear relationship between the maximum lateral deformation on the pile top and the pile inclination is proposed. The outcome of this study may be helpful for understanding the lateral deformation behaviour of piles in calcareous sand and designing inclined piles.

Reliability analysis and risk assessment of deep excavations using random-set finite element method and event tree technique

In the recent past years, the importance of reliability analysis and risk assessment in solving Geotechnical Engineering problems is underlined in literature. This study is aimed to show the feasibility of Random Set Finite Element Method (RS-FEM) and Event Tree Analysis (ETA) in assessing the reliability and risk to fatality of urban excavations. In order to fulfill this aim, a case study (22-meter excavation) which is stabilized with soil anchors is considered in North of Tehran, Iran. Prior to risk assessment, the failure probability of the deep excavation is estimated using RS-FEM, which is a relatively novel method in analyzing the reliability of deep excavations. Findings of the reliability analysis suggest that the upper and lower bounds of failure probabilities (Pf) for the considered case study are 0.0002 and 0.00001, respectively. Subsequently, using ETA, different possible scenarios, which may lead to fatality, are defined and proper probabilities are assigned to each scenario. Finally, for risk quantification purposes, the outcome probability of each scenario is multiplied by a considered Value of Statistical Life (VSL) as well as an aversion factor. Overall, findings recommend that the presented methodology (i.e. RS-FEM coupled with ETA) can be employed for Quantitative Risk Assessment (QRA) in deep urban excavations. Nevertheless, further research is recommended for other case studies as practicing the aforementioned method can constitute common sense on QRA of deep excavations.

Probabilistic Bearing Capacity Prediction of Square Footings on 3D Spatially Varying Cohesive Soils

The bearing capacity of square and/or rectangular footings in geotechnical foundation designs traditionally is determined based on experimental observations and/or deterministic analysis assuming uniform soil profiles. However, soils are spatially varying, and this spatial variability can significantly affect the bearing capacity of the foundation soils. Probability-based design methods can address this problem explicitly. However, a full three-dimensional (3D) probabilistic simulation, such as that involving the random finite-element method, generally is prohibitive, because it involves numerous Monte Carlo runs of a complicated nonlinear elastoplastic algorithm. This paper developed and validated an approximate analytical method based on local averaging theory and geometric averages of soil properties directly under the footing. It was found that the theoretical prediction of the first two moments of a square footing bearing capacity agrees very well with crude Monte Carlo simulation. The analytical prediction of the probability of a design failure was validated through simulation and can be used directly in reliability-based designs against bearing failure.

Improved Vanmarcke analytical model for 3D slope reliability analysis

This paper presents an improved algorithm for evaluating the reliability of three-dimensional soil slopes based on the Vanmarcke model (VM). In the development of the improved Vanmarcke model (IVM), the sliding mass is assumed to be a portion of a cylinder bounded by two ellipsoidal end sections. The soil spatial variability of both the cylindrical and ellipsoidal sections is considered. A set of equations is derived to determine critical failure surfaces and compute their reliability indices. Numerical studies are performed to examine the IVM. The results indicate that (1) the IVM predicts a similar critical failure length compared with that computed by the VM. However, a lower reliability index is obtained by the former. (2) The relative difference between the reliability indices computed by the two analytical models can reach 20% for practical situations. The horizontal scale of fluctuation (SOF) of soil properties is the main factor affecting the relative difference. (3) Compared to the random finite element method, the IVM still gives unconservative analysis results, especially at low horizontal SOFs. This is due to the prediction of smaller critical failure lengths by the IVM for small horizontal SOFs and some retained assumptions of the VM when developing the IVM.

Analyses of the Impacts of Climate Change and Forest Fire on Cold Region Slopes Stability by Random Finite Element Method

Increasing number of landslides occurred in the cold regions over the past decades due to rising temperature or forest fires associated with climate change. The instability of thawing slopes caused serious damages to transportation infrastructure, residential properties, and losses of human lives. These types of landslides, however, are difficult to analyze by the traditional limit equilibrium methods due to the coupled thermos-hydro-mechanical multiphysics processes involved. This paper describes a novel microstructure-based random finite element model (RFEM) to simulate the stability of permafrost slope subjected to climate change, including the increasing extent of thawing by warm atmosphere and thermal load due to forest fire. The properties of frozen soil are captured with random finite element model incorporating soil-phase coding. The thermomechanical responses of a permafrost slope are simulated to obtain the temperature, displacement, and stress fields. From these, the local factors of safety are obtained, which predict failure slumps along the slope that are consistent with the field-observed failure behaviors in permafrost slopes. The effects of climate change on the permafrost slope stability are analyzed for the years of 1956, 2017, and 2045. The results demonstrated appreciable amount of effects of climate change on the extent of slope failure zones. Forest fire led to melting of frozen soil and also affects the slope stability primarily in the shallow depth.

Probabilistic analysis of the diaphragm wall using the hardening soil-small (HSs) model

The main goal of this article is to perform a probabilistic analysis on a cantilever diaphragm wall constructed in sandy subsoil characterized by spatially variable strength and stiffness parameters. Three quantitates are considered, namely, the deflection of the wall, the settlements behind the wall and the maximum bending moment along the wall. To enable high accuracy of the evaluation of these quantities, a hardening soil model with a small strain overlay is used. To account for soil spatial variability, the friction angle of the sand is modelled using an anisotropic random field with specified vertical and horizontal scales of fluctuation (SOFs). All computations of the considered boundary value problem are carried out by means of the random finite element method (RFEM). The influence of both the vertical and horizontal SOFs on the probabilistic distributions of all the considered quantities is investigated. Reliability analyses are carried out based on the obtained distributions. Additionally, the effect of the number of realizations in the simulation process is analysed. It is shown that in the case of a diaphragm wall, the value of the horizontal SOF can substantially affect the probability of both excessive deformations as well as high bending moment values. It is also shown that additional modelling of soil stiffness moduli by a random field may induce small but noticeable changes in the probability of exceeding the conditions of the serviceability limit state.

Structural Responses of Statically Indeterminate Beams Induced by Soil Spatial Variability

The effect of the soil spatial variability on the structural assessment is explored in a context of statically indeterminate beams. The differential settlement among the four footings of a continuous beam is probabilistically determined considering various levels of soil spatial variability using the random finite element method. The settlement-induced beam internal forces, in terms of the transverse shear force and bending moment, are solved by using the force method. The variation of shear force and bending moment within a statically indeterminate beam, which is induced by the soil spatial variability, is systematically quantified using this probabilistic framework. This study points to the importance of properly addressing the effect of spatially varied soil conditions on structural design and promotes the integrated geotechnical and structural design.

Mobilisation-based characteristic value of shear strength for ultimate limit states

ABSTRACT Spatial variability in soil shear strength affects the occurrence of the ultimate limit state not only by the spatial averaging along the potential slip curve but also by seeking out mechanically admissible weak zones. The former factor (spatial averaging) reduces the variance of the mobilised shear strength, whereas the latter factor (weak-zone seeking) reduces the mean of the mobilised shear strength among others. Existing simplified formulas for determining the characteristic value of shear strength consider statistical spatial averaging only, not weak-zone seeking. This paper calibrates the weakest-path model (WPM) using simulation results from the random finite element method (RFEM). The calibrated WPM captures both spatial averaging and weak-zone seeking. Moreover, the behaviours for the calibrated WPM are similar to those for the RFEM. Based on the calibrated WPM, a simplified formula is proposed to determine a mobilisation-based characteristic value. The effectiveness of this formula is showcased by real case studies. It is found that for problems whose uncertainty is dominated by spatial variability and whose slip curve is not highly constrained by mechanical admissibility, the proposed formula provides significant improvements over existing simplified formulas in the literature that consider only statistics and do not consider mechanics at a detailed level.

Slope stability analysis considering the rotated anisotropy in soil properties

PurposeThis paper aims to analyze the influence of rotated anisotropy on the stability of slope, the random finite element method is used in this study.Design/methodology/approachThe random field is generated by the discrete cosine transform (DCT) method, which can generate random field with different rotated angles conveniently.FindingsTwo idealized slopes are analyzed; it is observed that the rotated angle significantly affects the slope failure risk. The two examples support the conclusion that when the orientation of the layers is nearly perpendicular to the slip surface, the slope is in a relative stable condition. The results of heterogeneous slope with two clay layers demonstrate that the rotated angle of lower layer mainly controls the failure mechanism of the slope, and the rotated angle of upper layer exhibits a significant influence on the probability of slope failure.Originality/valueThe method for rotated anisotropy random field generation based on the DCT has a simple expression with few parameters and is convenient for implementation and practical application. The proposed method and the results obtained are useful for analyzing the stability of the heterogeneous slopes in engineering projects.

Probabilistic simulation of entire process of rainfall-induced landslides using random finite element and material point methods with hydro-mechanical coupling

Rainfall-induced landslides are a major geohazard worldwide, which involve a complicated process, starting from rainfall infiltration, to landslide triggering and initiation, and post-failure large deformation of soils. To effectively mitigate landslide hazards, quantitative risk assessment (QRA) of landslides may be performed, which includes assessment of landslide probability and consequences. Because rainfall-induced landslide probability is controlled by rainfall infiltration and landslide triggering, while landslide consequences are often dictated by post-failure large deformation of soils, it is necessary to model the entire process of a landslide in QRA. However, most previous QRA studies did not model the entire landslide process (e.g., without modeling of rainfall infiltration or post-failure large deformation of soils) due to the difficulty of slope stability analysis methods (e.g., limit equilibrium methods and finite element method (FEM)) in modeling large deformation of soils. This study proposes a probabilistic method for simulating the entire process of rainfall-induced landslides considering spatial variability of soil properties. A two-stage method containing FEM and material point method (MPM), both with hydro-mechanical coupling, is proposed to simulate a landslide from triggering by rainfall to post-failure large deformation of soils. It quantifies landslide probability and consequences simultaneously and provides new insights for QRA of rainfall-induced landslides.

Novel approach to efficient slope reliability analysis in spatially variable soils

The random field finite element method (RF-FEM) provides a robust tool for carrying out slope reliability analysis that incorporates the spatial variability of soil properties. However, it has a major drawback of being computationally very time-consuming. To address this common criticism, the current study proposes a novel metamodel-based method for efficient slope reliability analysis in spatially variable soils. The proposed method involves the use of Convolutional Neural Networks (CNNs) as metamodels of the random field finite element model. With proper training using a small but sufficient number of random field samples, the CNN can potentially replace the computationally demanding random field finite element analyses for Monte-Carlo simulations. This paper examines the capability of CNNs to learn high-level features that contain information about the random variabilities in both spatial distribution and intensity, and the accuracy of the subsequent predictions of the RF-FEM results. Application of the proposed method to slope reliability analysis in spatially variable soils is illustrated and compared against other metamodel-based approaches, using a case study involving a multi-layered soil system with randomly varying cohesion c and the friction angle ϕ. The results show that (i) the proposed CNN approach predicts a probability of slope failure that is within 5% of the corresponding value obtained using direct RF-FEM Monte-Carlo simulations, but at a small fraction of the computational cost, and (ii) the proposed method also compares favourably against other metamodel-based methods in terms of computational efficiency and accuracy.

Probabilistic Settlement Analysis of Strip Footing on Spatially Random Soil

The prediction of settlement in a traditional design approach usually uses a deterministic value of modulus of elasticity (E), which is estimated as an average value by testing the soil at selected locations. However, these deterministic properties of soil may not represent the actual properties of soil and site condition. Due to numerous sources of uncertainty, the properties of soil mass are spatially varying and anisotropic in the natural field condition. In this study, a random finite element method (RFEM) is used to evaluate the reliability of settlement of the strip footing on spatially random soil. Modulus of elasticity is the only considered random parameter. For this purpose, 2000 spatially random realizations of E-field are generated using Monte Carlo Simulation. Each of these realizations of heterogeneous soil profile is passed to FEM to analyze the settlement of footing. The final settlement results measured in all these realizations are then statistically evaluated and compared. The results of analysis show that the mean and standard deviation of the footing settlement are increased with increasing spatial correlation length. The large value of isotropic correlation length led to an increase in the mean settlement value by more than 25% as compared with the deterministic settlement calculations. Also, it is concluded that the rate of increase of settlements for anisotropic correlation length is lower than the one under isotropic condition.

Probabilistic risk assessment of landslide-induced surges considering the spatial variability of soils

Quantitative risk assessment of landslide-induced surges is often a prerequisite for formulating rational strategies to reduce the disaster severity degree of surrounding residents and infrastructures facilities. In this study, soils are simulated by a random field and the random finite element method is utilized to obtain several relevant parameters (e.g., volume of slide mass, slide velocity, inclination angle and length of slip surface) of reservoir bank slopes for evaluating the landslide-induced surges hazard. A modified risk index is proposed to evaluate the landslide-induced surges hazard, which is more straightforward than the initial surge height. Quantitative risk assessment is conducted based in the introduced risk index for the occurrence of reservoir bank landslides. Compared with a uniform soil slope, a slope considering spatially variable soils generally has a higher initial surge height, which implies a more disastrous surge hazard.

Influence of the Spatial Variability of Soil Shear Strength on Deep Excavation: A Case Study of a Bangkok Underground MRT Station

This paper investigates the effects that the spatial variability of a soil's undrained shear strength has on lateral wall movements and ground surface settlements when performing a deep excavation stability analysis. A random finite-element method is employed to statistically assess a deep excavation. A case study based on an actual deep excavation project in Bangkok's subsoils was used to validate the methodology. The two-dimensional spatial variability of the undrained shear strength in the clay layers of Bangkok's subsoil is simulated using the random field theory and Monte Carlo simulation. The Mohr–Coulomb model is used to predict lateral wall movements and ground surface settlements, while the stability analysis of the deep excavation is evaluated by the factor of safety using the strength reduction approach. The results show that spatial variability highly affects the distribution of lateral wall movements and ground surface settlements, as well as the scatter of the factor of safety corresponding to progressing stages of excavation.

Probabilistic undrained bearing capacity of skirted foundations under HM combined loading in spatially variable soils

The behaviour of skirted foundations subjected to combined vertical (V), horizontal (H) and moment (M) loading is of particular interest to the geotechnical engineers. The bearing capacity of skirted foundations under combinations of VHM loading is represented by failure envelopes, which is commonly used in its stability assessment. In current studies, failure envelopes for skirted foundations were established deterministically, ignoring the spatial variability of natural soils. The paper aimed to investigate the probabilistic failure envelope of skirted foundations in the presence of soil undrained shear strength linearly increasing with depth. Random finite element method (RFEM) combining with random field theory, finite element method and Monte Carlo simulation was conducted to evaluate the uniaxial bearing capacities and define the HM failure envelopes. The influence of spatial variability on the stochastic response of bearing capacity in the HM space was discussed.

Quantifying installation risk during spudcan penetration

Installation of a mobile jack-up rigs with spudcan foundations are sometimes challenge due to uncertain offshore environments. Prediction of penetration resistance during installation is often necessary to avoid hazards such as punch-through failure. When the field monitored data deviates with these predictions, engineers have to decide how severe this deviation is based on their experience. This paper provides a method that can quantify the installation risk by a set of percentile curves of penetration resistance against depth. The percentile curves can be quantified through combining a random large deformation finite element method with Monte-Carlo simulation. The spatial variability in seabed soils can be considered and the penetration resistance curves through the random soils can be obtained. This model was verified by a spudcan installation penetration into deeper seabed. Finally, four field cases in North-East Brazil and Gulf of Mexico are investigated. Results show that the installation risk during spudcan installation can be estimated by comparing the measured preloading and penetration depth values with the percentile curves, which indicates the proposed method is capable to help decision making during spudcan installation.

Microstructure-Based Random Finite Element Method Model for Freezing Effects in Soils and Cold Region Retaining Walls

This paper describes the development of a random finite element model that allows holistic simulation of the phase transition and consequent development of internal stress and volume changes in frozen soils. The simulation capabilities of the model are first validated with laboratory scale experiments. The validated model is then implemented to study the soil lateral stress on the retaining wall subjected to frost action. The results show that the frost action leads to an increase of lateral stresses along the retaining wall. Strategies to mitigate the frost loads on the retaining wall are analyzed with this model; drainage of water in the backfill and use of thermal insulation layer both help to mitigate the lateral frost loads. Overall, by accounting for the spatial nonhomogeneity and coupled thermo-mechanical responses in frozen soils, the model provides holistic simulation of the responses of retaining walls subjected to freezing conditions.

Risk-Based Decision Making Method for Selecting Slope Stabilization System in an Abandoned Open-Pit Mine

Background:The construction and stabilization of deep excavations are associated with several uncertainties due to heterogeneous geological conditions. Therefore, the conventional methods of slope stability analysis do not provide reasonable results.Aim:Hence, it is logical to perform reliability analysis and also risk assessment to make a wiser decision under uncertainty for choosing the proper stabilization method of slopes.Methods:In this regard, a real case study, a 50-meter-deep abandoned open-pit mine, is considered. In the past, the studied deep excavation was located in a rural area, away from the important structures. However, due to the development of the city, the open-pit mine is now located in the city. Furthermore, the Kan River is located on the eastern side of the excavation. Deterministic analysis showed that that Factor of Safety is not sufficient for permanent condition; thus, the deep excavation may have destructive impacts on the adjacent structures and infrastructures by putting them in danger in the case of failure.Results:These circumstances resulted in using reliability analysis and risk assessment using non-deterministic approach. Random Set Finite Element Method (RS-FEM), a non-probabilistic method, is used in determining how much the slope is reliable. The upper and lower bounds of probability of excessive displacement and probability of failure are obtained using RS-FEM by Plaxis2D software. Afterward, HAZUS is successfully used to quantify the economic risk of different stabilization alternatives by defining various scenarios in order to consider the consequences of excavation failure on adjacent utilities and infrastructures.Conclusion:The best alternative is defined as the stabilization method with the lowest economic risk. As a result, it is noticeable that this paper provides a comprehensive methodology for decision making, based on reliability analysis and risk assessment, in stabilizing slopes.

Procedures for quick estimation of hydraulic conductivity of unsaturated soils

This paper describes a heuristic approach that combines a limited number of experimental measurements with the random finite-element method (RFEM) to accelerate significantly the process of measuring the hydraulic conductivity of unsaturated soils. A microstructure-based RFEM model is established to describe unsaturated soils with distribution of phases based on their respective volumetric contents. The intrinsic hydraulic properties of each phase (soil particle, water and air) are applied based on the microscopic structures. The intrinsic permeability of each soil phase is first calibrated from soil measured under dry and saturated conditions, which is then used to predict the hydraulic conductivities at different extents of saturations. The results match closely the experimental data. The pore size parameter was obtained from the variations in hydraulic conductivity with degree of saturation; from this, the soil-water characteristic curve (SWCC) is predicted. The results show that the SWCC estimated matches very well with experimental data. Overall, this study provides a new modelling-based approach to predicting the hydraulic conductivity function and SWCC of unsaturated soils based on measurement at completely dry or completely saturated conditions. An efficient way to measure these critical unsaturated soil properties will benefit introducing unsaturated soil mechanics into engineering practice.

Probabilistic Analysis of Slopes with Linearly Increasing Undrained Shear Strength Using RLEM Approach

Shear strength parameters in naturally alluvial deposits bear variation with depth (non-stationarity). Probabilistic analysis of simple slopes with linearly increasing (mean) undrained shear strength with depth and spatial variability is explored using the 2D random limit equilibrium method (RLEM) along with the non-circular failure surface assumption. A deterministic factor of safety design chart method is extended to express margins of safety as probability of failure for soils with random variability and positive correlation between shear strength parameters and unit weight. The effects of isotropic and anisotropic spatial variability and cross-correlation of soil properties on probability of failure are also investigated. Combinations of low correlation length and positive cross-correlation between strength parameters are shown to reduce the probability of failure. This offers the possibility to bring probabilistic estimates of failure into alignment with expectations of slope stability based on experience with factors of safety. The results of a limited number of RLEM analyses are compared with some other results using the 2D random finite element method (RFEM). The influence of different involved parameters and assumptions, more specifically the nonlinear variation of the undrained cohesion and also the non-circular slip surface, on the embedded uncertainty and probability of failure was elaborated. The research has emphasized the importance of non-circular failure surface assumption along with the consideration of non-stationarity in shear strength parameters.