International Journal of Geomechanics

Published by American Society of Civil Engineers
Online ISSN: 1532-3641
Publications
Topographic (top) vs statigraphic (bottom) seismic wave amplification: example in Caracas, Venezuela (Semblat et al., 2002). 
Numerical wave dispersion for various finite element orders: linear (top), quadratic (middle) and fourth-order (bottom) (Semblat 2000b). 
Article
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.
 
Lake Nyos is a deep crater lake in Cameroon (top figure). In 1986, huge amounts of carbon-dioxide gas were released from the lake possi- bly due to seismic tremors. A mix of carbon-dioxide and water erupted 120 meters above the lake with a speed of roughly 100 kilometers per hour. This displaced oxygen resulting in asphyxi- ation of more than 1,700 people and 3,000 cattle as far as 23 kilometers from the lake (bottom figure). [Source: ] 
Elementary volume of the porous material δV , and the volume occupied by the i-th constituent δV (i) (i = 1, · · · , N ).
Numerical coupling algorithms: fully coupled (top left), lockstep (top right), subcycling (bottom left), and Jacobi (bottom right).
Verification by a manufactured solution: minimum error vs. global convergence tolerance, ǫ l or ǫ j. The error is measured as the L 2-norm of the computed solution minus the exact solution and the minimum is taken over the total solution time.
Verification by a manufactured solution: number of iterations vs. global convergence tolerance, ǫ l or ǫ j. The number of iterations is measured as the number of fluid and solid solves per solution cycle before the global tolerance is met.
Article
In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interacting continua. In its most general form, this framework provides a mechanism for capturing multiphase flow, deformation, chemical reactions and thermal processes, as well as interactions between the various physics in a conveniently implemented fashion. To simplify the presentation of the framework, results are presented for a particular model than can be seen as an extension of Darcy's equation (which assumes that the porous solid is rigid) that takes into account elastic deformation of the porous solid. The model also considers the effect of deformation on porosity. We show that using this model one can recover identical results as in the framework proposed by Biot and Terzaghi. Some salient features of the framework are as follows: (a) It is a consistent mixture theory model, and adheres to the laws and principles of continuum thermodynamics, (b) the model is capable of simulating various important phenomena like consolidation and surface subsidence, and (c) the model is amenable to several extensions. We also present numerical coupling algorithms to obtain coupled flow-deformation response. Several representative numerical examples are presented to illustrate the capability of the mathematical model and the performance of the computational framework.
 
Vertical drain parameters
Selected soil parameters in 2D and 3D FEM analysis
Article
This paper presents a three-dimensional (3D) and two-dimensional (2D) numerical analysis of a case study of a combined vacuum and surcharge preloading project for a storage yard at Tianjin Port, China. At this site, a vacuum pressure of 80 kPa and a fill surcharge of 50 kPa was applied on top of the 20m thick soft soil layer through prefabricated vertical drains (PVD) to achieve the desired settlements and to avoid embankment instability. In 3D analysis, the actual shape of PVDs and their installation pattern with the in-situ soil parameters were simulated. In contrast, the validity of 2D-plane strain analysis using equivalent permeability and transformed unit cell geometry was examined. In both cases, the vacuum pressure along the drain length was assumed to be constant as substantiated by the field observations. The finite element code, ABAQUS, using the modified Cam-clay model was used in the numerical analysis. The predictions of settlement, pore water pressure and lateral displacement were compared with the available field data, and an acceptable agreement was achieved for both 2D and 3D numerical analyses. It is found that both 3D and equivalent 2D analyses give similar consolidation responses at the vertical cross section where the lateral strain along the longitudinal axis is zero. The influence of vacuum may extend more than 10m from the embankment toe, where the lateral movement should be monitored carefully during the consolidation period to avoid any damage to adjacent structures.
 
Article
[Extract] This Special Issue of the Int. J. Geomech. on soft clay engineering and soft clay improvement is a result of discussion among various colleagues during the Geo-2000 Conference in Melbourne, where the need for a Special Issue on soft clay engineering and improvement was raised. The papers contributed to this Special Issue are selected to reflect the latest developments relating to soft clay engineering and improvement, and address research and applications in many places around the world ~e.g., Australia, Finland, The Netherlands, Norway, Singapore, United Kingdom, and the United States!. This Special Issue covers a variety of aspects for soft clay engineering and improvement, including constitutive modeling, numerical and analytical methods, design parameters, field and laboratory testing, and case studies.
 
Article
This paper describes the analytical formulation of a modified consolidation theory incorporating vacuum pressure, and numerical modelling of soft clay stabilized by prefabricated vertical drains, with a linearly distributed (trapezoidal) vacuum pressure for both axisymmetric and plane strain conditions. The effects of the magnitude and distribution of vacuum pressure on soft clay consolidation are examined through average time-dependent excess pore pressure and consolidation settlement analyses. The plane strain analysis was executed by transforming the actual vertical drains into a system of equivalent parallel drain walls by adjusting the coefficient of permeability of the soil and the applied vacuum pressure. The converted parameters are incorporated in the finite element code ABAQUS, employing the modified Cam-clay theory. Numerical analysis is conducted to study the performance of a full-scale test embankment constructed on soft Bangkok clay. The performance of this selected embankment is predicted on the basis of four different vacuum pressure distributions. The predictions are compared with the available field data. The assumption of distributing the vacuum pressure as a constant over the soil surface and varying it linearly along the drains seems justified in relation to the field data. Yes Yes
 
Article
A fluid-filled cylindrical cavern of circular cross section in a homogeneous infinite fluid-saturated polycristalline (salt) formation subjected to isotropic stress is set under internal pressure that differs from the confining pressure. The fluid in the cavern and in the mixture is treated as ideal and the solid as elastic. The state of stress that is established as a consequence of an outside pressure and a cavern pressure serves as the reference state. Perturbing the cavern pressure induces small changes in the solid and fluid densities and in the solid displacements. We compute these and other fields as functions of the radial distance from the cavern center and show that, depending on the relative stress levels, the (salt) formation experiences either a dilatation or a compaction that is highly concentrated in a thin boundary layer near the cavern wall and tapers off as one moves away from it. The amount of dilatation/compaction of the cylindrical wall and the thickness of the boundary layer grow with an increase in the difference between the referential confining pressure and the pressure in the cavern.
 
Article
This paper addresses the requirements of the dynamic models of the cable shovel underlying the ISE technology. The dynamic equations are developed using the Newton?Euler techniques. These models are validated with real-world data and simulated in a virtual prototype environment. The results provide the path trajectories, dynamic velocity and acceleration profiles, and dimensioned parameters for optimum feed force, torques and momentum of shovel boom-dipper assembly for efficient excavation. The optimum digging forces and resistances for the cable shovel excavators are modeled and used to predict optimum excavation performance. Ce document traite des exigences propres aux modèles dynamiques de la pelle à câbles, qui sont sous-jacentes à la technologie ISE. Les équations dynamiques sont développées au moyen des techniques Newton?Euler. Ces modèles sont validés par des données du monde réel et simulés dans un environnement prototype virtuel. Les résultats obtenus fournissent les trajectoires, les profils de vélocité dynamique et d'accélération, ainsi que les paramètres dimensionnés pour une force d'avance, des couples et des forces d'impulsion optimum des ensembles flèche principale-benne creusante, aux fins de l'efficacité du creusage. On modélise et utilise pour prédire la performance d'excavation optimale les données de force et de résistance de creusage optimum pour les pelles à câbles. RES
 
Article
Published comparisons of complex moduli in dry and saturated soils have shown that viscous behavior is only evident when a sufficiently massive viscous fluid (like water) is present. That is, the loss tangent is frequency dependent for water saturated specimens, but nearly frequency independent for dry samples. While the Kelvin-Voigt (KV) representation of a soil captures the general viscous behavior using a dashpot, it fails to account for the possibly separate motions of the fluid and frame (there is only a single mass element). An alternative representation which separates the two masses, water and frame, is presented here. This Kelvin-Voigt-Maxwell-Biot (KVMB) model draws on elements of the long standing linear viscoelastic models in a way that connects the viscous damping to permeability and inertial mass coupling. A mathematical mapping between the KV and KVMB representations is derived and permits continued use of the KV model, while retaining an understanding of the separate mass motions.
 
Article
Deep excavation often causes displacement of adjacent structures. Hence, necessary construction measures must be taken in order to minimize such disturbances. Appropriate construction measures depend on effective and reliable estimation of the induced ground movement during an excavation. This paper presents a systematic procedure, referred to as "information feedback analysis," which is used to predict excavation-induced deformation by collecting field information, such as displacements. With the use of optimization algorithms, the analyses result in a "best set" of soil parameters. These back-calculated soil parameters are then used to predict the deformation in the subsequent stages, one stage at a time, until the end of the excavation, which result in additional updated information continuously entered into the system, and hence, the prediction becomes progressively more and more accurate. This study has shown that the proposed approach exhibits at least two advantages over the conventional analysis. First, the use of field instrumentation to estimate geotechnical parameters allows the engineer to account for the global response of a soil-structure system. Second, since the information is collected throughout the length of construction, any departure from the original design should be reflected by the updated information, while the conventional analyses are conducted in the design stage only and always assume that construction proceeds as planned.
 
Article
Changes in soil pore volume and shape in response to internal and external mechanical stresses alter key soil hydrologic and transport properties. The extent of these changes is dependent on details of pore shape and size evolution. We present a model for quantifying rates of deformation and shape evolution of idealized spheroidal pores as functions of macroscopic stresses and soil rheological properties. Previous solutions for shrinkage of spherical pores embedded in a viscoplastic matrix under isotropic stress were extended to spheroidal pore shapes and biaxial stresses using Eshelby's classical theory. Bulk soil behavior was obtained from upscaling of detailed single pore deformation. Results show that pore closure rates increase with decreasing initial aspect ratio (i.e., oblate pores close faster than spherical pores), and with higher deviatoric stress. Incomplete pore closure is attributed to soil hardening due to pore shape accommodation under biaxial stresses. The model provides a means for approximating pore deformation as input to predictive models for soil hydraulic properties.
 
Article
The hydraulic shovel excavator has found significant applications in surface mining, construction, and geotechnical operations due to its flexibility and mobility. The key to high availability and utilization of this shovel is adequate understanding of machine dynamics and machine-formation interactions among other technical, operating, safety, and economic factors. These shovels are capital intensive, complex in design and operation within severely constrained environments. Detailed dynamic modeling and analysis are required to understand their effective utilization for achieving efficient operating performance and economic useful lives. Previous attempts at solving these problems are limited because they do not provide knowledge on the resistive forces and moments for efficient excavation. In this paper, the Newton-Euler techniques are used to develop hydraulic shovel dynamic models with numerical examples. Detailed analysis of the results shows that: (1) the kinematics of the stick-bucket joint (joint 3) is the most critical and effective control of this joint and is important input into efficient excavation design and execution; and (2) the highest resistive moments occur between the duration of 1.5 and 2.0 s after the start of formation excavation and the highest magnitudes are 1,500 Nm (for stick), 900Nm (for bucket), and 600Nm (for boom). Based on these results, the path trajectories, dynamic velocity and acceleration profiles, and dimensioned parameters for optimum feed force, torques, and momentum of shovel boom-bucket assembly can be modeled and used for efficient excavation. The optimum digging forces and resistances for the hydraulic shovel excavator can also be modeled and used to predict optimum excavation performance.
 
Article
The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studies. Both end restraint and partial drainage can cause bulging of the triaxial specimen around mid-height. Inhomogeneities due to partial drainage influence the stress-strain behavior during destructuring, a characteristic feature of a structured soil. With an increase in the strain rate, the change in voids ratio during destructuration reduces, but, in contrast, the mean effective stress at which destructuration commences was found to increase. It is shown that the stress-strain behavior of the soil calculated for a triaxial specimen with inhomogeneities, based on global measurements of the triaxial response, does not represent the true constitutive behavior of the soil inside the test specimen. For most soils analyzed, the deviatoric stress based on the global measurements is about 25% less than that for the soil inside the test specimen, when the applied axial strain is about 30%. Therefore it can be concluded that the conventional global measurements of the sample response may not accurately reflect the true stress-strain behavior of a structured soil. This finding has major implications for the interpretation of laboratory triaxial tests on structured soils.
 
Article
This article presents the use of neural networks for the prediction of movement of natural slopes. The aim is to predict velocity changes of a moving soil mass using climatological and physical data, such as rainfall and pore water pressure, which are used as input parameters in an artificial neural network (ANN). The network is designed to function as an alarm and is a decision-making tool for persons in charge of landslide monitoring. The raw data were obtained from a continuously monitored landslide, located in Sallèdes, near Clermont-Ferrand (France), and include daily precipitation, evaporation, pore water pressure, and landslide velocity values. The various networks used in this study are two layer perceptrons trained using the Levenberg-Marquardt algorithm, based on backpropagation of error. The most sophisticated model presented in this article was developed by cascading two recurrent networks of the same type. This model permits a satisfactory 3-day prediction of landslide velocity if quality data from continuous measurements are available. A simple example of the calculation of a safety factor for an unstable slope shows how neural techniques may be coupled to good advantage with purely mechanical models.
 
Article
Guadalquivir blue marl is a high-plasticity overconsolidated carbonate clay. This soil presents an elevated fragility and high susceptibility to moisture changes. These characteristics have caused many geotechnical accidents, such as the Aznalcollar dam failure, in Seville, Spain. A comprehensive test campaign was conducted to determine the physical and chemical properties of the blue marl. Analysis by scanning electron microscopy (SEM) and mercury intrusion porosimetry (MIP) allowed characterization of its internal structure, revealing clear differences between the macro- and microstructure. A novel one-dimensional (1D) model for predicting the volumetric deformation (under oedometric conditions) of the Guadalquivir blue marl with suction and vertical pressure changes was proposed. The model, based on data from shrink-swell tests, provided an acceptable estimation of the volumetric behavior of the soil with a relatively simple set of parameters. The results were experimentally verified by suction-controlled oedometer tests and showed an acceptable agreement with the data measured. The proposed model is valid for ranges of swelling, shrinkage or collapse.
 
Article
In geotechnical engineering, characterization of time-dependent behavior of clayey soils under one-dimensional (1D) constant stress has been controversial. In some special cases, the creep deformation is insignificant during primary consolidation, and is assumed to start at the end of primary consolidation. In the general case, the total deformation results from a coupled process involving both hydromechanical (mechanical loading) and viscous (creep) effects. Creep deformation commences at the start of the loading. This paper proposes a methodology to decouple the creep-deformation component from the total deformation measured in oedometer tests. This methodology is based on the concept of isotache [i.e., there exists a unique relationship among void ratio, effective stress, and time factor (Hypothesis B)]. The methodology was used to analyze the 1D compression data of reconstituted Regina clay samples. It was demonstrated that this methodology is capable of determining the intrinsic properties of a 1D normally consolidated curve (independent of sample thickness and duration of end of primary consolidation) and creep behavior.
 
Article
Based on imaging and the discrete element method (DEM), this study mainly aims to compare the two-dimensional (2D) and three-dimensional (3D) micromechanical modeling of the indirect tensile (IDT) tests for asphalt mixtures. The 2D and 3D microstructurebased discrete element models for the IDT test were established by a discrete element program. The strengths and stresses at low temperatures were simulated based on these models. The obtained results were compared and verified by an actual IDT test. The effects of stiffness and bond strength on the 3D simulation were also analyzed. Results show that the 3D discrete element simulation results are more stable and more reliable than the 2D discrete element simulation results. The model parameters influence the 3D discrete element simulation results, and different model parameters influence the strength and stress with respect to the IDT test at low temperatures to different extents.
 
Article
The vector-sum method (VSM) is advanced by considering the vector characteristics. As a cost of this advantage, a predefined global sliding direction is required, which has been a key issue for the application of the VSM. Although the VSM has been steadily refined since its initial version in 2008, limited progress on this issue has been achieved, and the global sliding direction is still prespecified by assumption. In the aim of solving this issue, this article proposes a rigorous analytical solution based on the principle of potential energy minimization. In addition, the VSM is improved by comparing the resisting moment with the driving moment at the moment center, which can be determined by the shape of the slip surface. Finally, this method is verified to be feasible by three classical earthen slopes with different soil composition. Compared with the solutions found by the rigorous Morgenstern-Price method with the half-sine function as the interslice force function, the calculated results demonstrate that the proposed method can accurately estimate slope stability.
 
Article
Within the framework of the limit equilibrium method of slices, a slope reliability analysis accounting for two-dimensional (2D) spatial variation requires a model to discretize a random field into a finite number of random variables. A careful review of the existing models has revealed that the models originally developed for homogeneous slopes suffer from certain shortcomings when applied to nonhomogeneous slopes, which have been taken care of in the refined models recently proposed by the authors. Further, on the two approaches followed in accounting for spatial variability, the paper examines the consequences of adopting the simplified approach based on a specific slip surface in place of the rigorous approach based on the probabilistic critical slip surface. Analyses of illustrative examples have revealed that an analysis based on a combination of an inappropriate discretization model and a simplified approach might result in errors as much as 65% on the nonconservative side. The paper also addresses the issue of obtaining solutions in slope situations in which site-specific values of the 2D scale of fluctuation are either not available or are different layerwise.
 
Article
Soil arching effect has been widely recognized as one of the most critical factors governing load-transfer mechanism in the design of various geotechnical infrastructures. However, most existing studies on soil arching effects are limited only to the state when soil arching effect is fully mobilized, while the knowledge about the evolution of soil arching effects with relative displacement remains largely unknown. In this study, a series of classical trapdoor tests are conducted to investigate the evolution of soil arching effects with the progressively developed relative displacement for the trapdoor problem. A particle image velocimetry (PIV) technique is employed to measure the progressive development of displacement and shear strain of soil mass. The development of slip surfaces as well as stress transfer in soil mass are studied. The observed evolution of slip surfaces in soil mass is then related to the load-displacement characteristics of the soil mass under various magnitude of surcharge during trapdoor tests. The test results indicate that the triangular and vertical slip surfaces correspond with the minimum and residual values of loosening earth pressure, respectively. Upon the experimental observations, analytical solutions are proposed to predict both the minimum and the residual values of loosening earth pressure acting on top of the trapdoor, where the deflection of principal stress axes is considered. Comparisons between the model predictions with test results are carried out. Good agreement is observed, which validates the proposed theoretical model.
 
Article
A discrete-element method (DEM)-based numerical model was developed to simulate the triaxial compression response of sand strengthened using microbially induced carbonate precipitation (MICP). A three-dimensional (3D) sphere packing algorithm that uses a particle-growth model was used to generate the initial assemblage of particles. A parameter identification approach was used to evaluate the five microscale parameters of the DEM model (two elastic and three rupture parameters) using experimental results from drained triaxial compression tests on sand. The interparticle friction angle was found to be the most influential of the five parameters with respect to modeling the constitutive response. A particle homogenization approach was used to model the particles when they are strengthened with low amounts of calcium carbonate (<1% by mass). The particle contacts are assigned a cohesive shear strength when higher amounts of calcium carbonate (>1% by mass) are present to model the effect of cementation between sand grains. This DEM model was shown to be capable of adequately simulating the drained triaxial compressive response of MICP-strengthened sands. The increase in microstructural heterogeneity as the carbonate content is increased was visualized through normal contact force distributions. The model can be used to estimate the desired level of cementation for the design of MICP treatment strategies with minimal experimentation.
 
Article
A novel, meshless numerical method, called general particle dynamics (GPD), is proposed to simulate the initiation, propagation, and coalescence of three-dimensional (3D), pre-existing penetrating and embedded flaws as well as size effects and large deformations of rock materials. On the basis of the nonlinear unified strength criterion, an elastic-brittle-plastic damage model was developed to reflect the initiation, growth, and coalescence of the 3D flaws and the macrofailure of rocklike materials by tracing the propagation of the cracks. Then, growth paths of cracks were captured through the sequence of such damaged particles. In this paper, the GPD code is applied to simulate the macrofailure, large deformation, and size effects of the heterogeneous rocklike materials. The present numerical simulations focus on the effects of sample sizes, the nonoverlapping length and types of flaws on the failure, and the complete stress-strain curves of the rocklike materials. The initiation, propagation, and coalescence processes of the wing cracks, the antiwing cracks, the oblique secondary cracks, the out-of-plane shear cracks, and the quasi-coplanar shear crack in a rocklike sample subjected to uniaxial compression is numerically simulated using GPD3D. The numerical results indicate that the nonoverlapping lengths and types of flaws significantly influence the coalescence types. The numerical results are in good agreement with the experimental results. It is proven that the GPD3D can adequately simulate the failure processes, large deformation, and size effects of the rocklike materials. DOI: 10.1061/(ASCE)GM.1943-5622.0000565.
 
Article
This paper investigates the effect of the anisotropy and nonhomogeneity of soil on the three-dimensional stability of a pressurized tunnel face. A three-dimensional horn failure mechanism was constructed. The energy dissipation of the ultimate limit state was analyzed, and the upper bound solution of collapse pressure was obtained according to the limit analysis theory. The validity of the proposed method was demonstrated by comparing its results with those from other researchers. The difference in collapse pressures at linear variation cohesion and average equivalent cohesion was analyzed in detail. It was found that the anisotropy and nonhomogeneity of soil cohesion have a great impact on the collapse pressure and failure scope of a pressurized tunnel face and thus should be properly considered in the support design of pressurized tunnels. In addition, an approximate solution for the collapse pressure of a tunnel face in nonhomogeneous soils is proposed based on Terzaghi’s method, which provides a simple method to quickly and effectively assess the stability of a pressurized tunnel face.
 
Article
A lack of joint specimens with the same natural surface morphology has limited detailed experimental study of the shearing performances of joints. In this technical note, we propose a way to batch-produce rock joints with the same natural surfaces by way of three-dimensional (3D) optical scanning of original rock joint specimens to gain their digitally natural geometry and then 3D rigid engraving. We also present a method for characterizing the shear damage of a natural rock joint. Manufacturing practice for sandstone, marble, and granite joints demonstrates its advantages in reliable precision for joint surface geometry and high efficiency for joint fabrication. At the same time, direct shear tests for the manufactured rock joint specimens indicate that the engraved rock joint can provide stable experimental results. Further analysis of microwearing damage to engraved natural rock joints after shear tests show that the wearing damage to natural rock joints under direct shear testing mainly happens at some local zones with high positive dip angles. These production examinations and experimental certifications indicate that our method can overcome the “bottleneck” difficulty in insufficient joint specimens with the same natural surface morphologies for experimental study, and provide a new way to quantitatively assess a joint’s shear damage.
 
Article
Three-dimensional (3D) slope stability analysis is a present research interest for geotechnical engineering. This work established a new 3D limit equilibrium method (LEM) to solve 3D slope stability with general-shaped slip surfaces. In the proposed method, a simple initial normal stress on a slip surface is used by analyzing the stresses on a vertical microcolumn. To ensure the accuracy of the results, a dimensionless variable is adopted to amend the initial normal stress. Then, by using the Mohr-Coulomb (M-C) criterion, the shear stress on the slip surface is also assumed. Different from the traditional LEM, global limit equilibrium (LE) conditions are used to avoid the effect of intercolumn forces on slope stability. Moreover, the Cartesian coordinate system is constructed on the basis of the main direction of a 3D sliding body; thus, strict solutions of 3D slope stability can be achieved with only three equations of static equilibrium on the sliding body. After contrasting the results in several classic slope examples, the proposed method's feasibility is verified with the following advantages: (1) it has a simple derivation process to obtain rigorous results, and compared with the same simple 3D nonrigorous method, the improvement of more than 10% on the slope factor of safety (FOS) is achieved; (2) it is easy to program with a fast solution speed, and compared with the conventional 3D Morgenstern-Price (M-P) method, the calculation speed is increased more than 1.5 × and (3) it can directly obtain the distribution of normal and shear stress on the slip surface and can also visually draw the global and local sliding trends of a 3D sliding body.
 
Article
The use of structural and nonstructural overlays has gained popularity in recent years due to financial and environmental constraints; however, the impact of overlay thickness and the type of applied tack coat on induced strains, where overlay interfaces with an existing surface layer, has not yet been extensively evaluated. In this study, the three-dimensional (3D) finite-element modeling technique was used to evaluate existing pavements of varying thicknesses with various overlay thicknesses, and different interface bonding strengths that were modeled in Abaqus. The results of this study verify that the impact of interface bonding strength on the overlay durability and structural characteristics of pavement changes drastically by changing the overlay thickness. For nonstructural overlays with a thickness of 12.7mm (0.5 in.) or 25.4mm (1 in.), interface bonding strength (tack coat) was found to play a prominent role in overlay durability, whereas overlay thickness was found to have a negligible impact. Increasing the thickness of the overlay from 25.4mm (1 in.) to 50.8mm (2 in.) significantly decreased the impact of interface bonding strength, whereas the influence of overlay thickness increased.
 
Article
In slope stability analysis, there are two commonly used methods for calculating the factors of safety (FS). The first is the strength reduction method (SRM), which defines the FS as the ratio of the real material shear strength to the critical shear strength in the limit equilibrium state. The second is the gravity increase method (GIM), which defines the FS as the ratio of the critical increased gravity to the actual gravity. On the basis of a kinematically admissible three-dimensional (3D) failure mechanism, this paper develops a framework to compare these two kinds of FS. Earthquake effects are included in the study by using the quasi-static representation. By means of the kinematic approach of limit analysis, the GIMcan give an explicit function about the FS, while the SRMcan only provide an implicit equation on the FS. The lowest solutions for both two kinds of FS are obtained by optimizing the variables from the 3D failure mechanism. Numerical results are calculated and presented in the forms of graphs to show the difference between these two kinds of FS. It is shown that the FS calculated by the SRM is equal to that calculated by the GIM when the slope is in the limit state (FS = 1.0), that the FS by the SRM is greater than that by the GIM for an unstable slope (FS < 1.0), and that the FS by the SRMis smaller than that by the GIMfor a safe slope (FS > 1.0). Finally, a power function is proposed to approximately express the relationship between these two kinds of FS.
 
Article
The failure criterion of rock material has been used in geotechnical engineering to assess the failure behavior of rocks under complicated stress conditions. In the present study, a new failure criterion is proposed; it takes into consideration the influence of intermediate principal stress for rock materials. The general characteristics of failure surface were analyzed, showing that the failure envelopes are convex and smooth everywhere except at the triaxial compression and triaxial tension conditions. A new shape function is presented to approach the failure criterion in the deviatoric plane, and the smoothness and convexity of the criterion is discussed. The new failure criterion is compared with some classic criteria by cross-sectional failure envelopes in the plane and meridian failure envelopes in the meridian plane, and the advantages of the new three-dimensional (3D) failure criterion are presented. The results show that the new criterion not only inherits the strength characteristic of the Hoek-Brown failure criterion at the triaxial compression condition, but it also predicts failure stress better than other 3D failure criteria for rocks under complicated stress states.
 
Article
Anchor foundations of various embedment ratios, shapes, and sizes are frequently used in civil engineering structures to provide uplift resistance. Therefore, to achieve economic and safe design of such foundations, engineers should understand the failure mechanism associated with them. In the present study, a three-dimensional (3D) finite element model incorporating an elastoplastic material model coupled with the isotropic strain-softening law, the nonassociated flow rule, and the shear-band effect, is used to investigate the failure mechanisms of vertically uploaded shallow rectangular anchor foundations buried in dense Toyoura sand. Satisfactory agreement was found between the experimental and numerical uplift resistance-displacement factor relationships. In particular, the peak uplift resistance, response stiffness, and passive plastic zone development are found to be functions of the embedment ratio, shape, and size. However, previous design approaches cannot capture the size effect on the peak uplift resistance factor of the rectangular anchor foundation. (C) 2012 American Society of Civil Engineers.
 
Article
The analysis of slope stability problems in engineering practice requires considerable attention for the three-dimensional (3D) effect of plan curvature of the slope. This paper quantifies this effect by a dimensionless parameter of the relative curvature radius of the slope (R/H) and proposes a set of 3D stability charts that can be used to estimate the factor of safety (FOS) of convex and concave slopes in plan view with homogeneous soil, extending those currently regularly used for 3D straight slope stability evaluations. To simplify the computational process, an alternative way to perform the FEM with the strength-reduction technique is used herein in the slope stability analysis. The strength-reduction analysis results in this paper together with results of other researchers were found to bracket the FOS to within ±5% or better and therefore can be used to benchmark the solutions of other methods. Changing the relative curvature radius of the slope (R/H) shows that concave slopes are more stable than straight slopes, but that convex slopes are less stable; moreover, the 3D effects are more significant in slopes with friction/cohesive soils with smaller values of R/H. Numerical 3D results are presented in the form of dimensionless graphs, which represent a convenient tool for practicing engineers to estimate the initial stability of excavated or artificial slopes.
 
Article
In this study, three-dimensional finite element models, incorporating an elastoplastic material model coupled with isotropic simple softening law, nonassociated flow rule, and shear-band effect, are validated for the evaluation of the shape effect of the square and rectangular vertically uploaded anchor foundations embedded in dense Toyoura sand with embedment ratio of 2 and width of 50 mm. The proposed numerical model has closely predicted experimental uplift load-displacement relationships. The shape effects on the results are also discussed in relation to the progressive failure around the foundations and the shape of the failure boundaries on the ground surface.
 
Article
This paper proposes three-dimensional (3D) simplified nonlinear methods for examining the soil–building interaction for nonlinear behavior of soils based on an input seismic wave field. A seismic wave field is defined as seismic waves propagating in a 3D medium. The proposed 3D methods were developed on the basis of the 3D linear method, which was recently proposed to adequately treat seismic surface waves trapped by a several-kilometer-deep underground structure. To demonstrate the feasibility of the proposed methods, interaction analyses of a midrise RC building and a wood building were performed in the reclaimed zone of Tokyo Bay in the cases of soils with linear, nonlinear, and liquefaction behavior for the 1923 Kanto earthquake. These interaction analyses provide a reasonable evaluation of building performance. In particular, building responses became excessively large, following extremely large increases in the amplitudes of surface waves in liquefied soils. The building responses provide significant clues for interpreting a typical damage pattern in which Japanese RC building damage is concentrated on the first story.
 
Article
In cylindrical coordinates, a potential method is developed for three-dimensional (3D) wave propagation in a poroelastic medium. By using the proposed potential method, the wave propagation problems can be reduced to the determination of four scalar potentials governed by four scalar Helmholtz equations, representing the motions of P1, P2, SV, SH waves in the porous media, respectively. By the methods of separation of variables, the general solutions to those Helmholtz equations are found in cylindrical coordinates. Boundary value problems associated with a homogeneous poroelastic half-space loaded by surface tractions, that is, Lamb's problem for a fluid-saturated medium is resolved using the obtained general solutions. It is shown that these potentials introduced in this research for 3D wave propagation problems can also be reduced to those reported by previous researchers for axisymmetric wave propagation in the fluid-saturated porous medium. Furthermore, numerical examples for the state-state and transient responses of the poroelastic half-space are provided.
 
Article
Resonant column (RC) testing is a widely used laboratory technique to determine the stiffness characteristics of soils under small- to medium-strain perturbations. Solid or hollow cylindrical soil specimens are set into motion in either torsional or longitudinal modes of vibration by an electromagnetic loading system whose frequency is changing until the first-mode resonant condition is reached, and then the shear modulus of soil is back-calculated from the fundamental frequency, the geometry of the specimen, and the end-restraint conditions. However, the outcomes of this test are largely affected by both the driving apparatus used for the specimen vibration and the motion-monitoring instruments lumped into a mass that oscillates with the specimen. This study presents the results pertaining to three-dimensional (3D) finite-differences (FD) simulations of RC tests on soil samples undergoing both torsional and longitudinal modes of vibration. The prime objective of the study was to examine the influence of the driving mass, the geometry of the specimen, the mode of vibration, and the boundary conditions on the RC test results. The numerical results show that the attachment of the instrumentation on the sample is the driving factor contributing to the error in the estimation of the soil dynamic characteristics, and typical equations for the calculation of the shear modulus from the resonant frequency in the longitudinal mode of vibration cannot be directly applied to their torsional-mode counterparts.
 
Article
One of the most important causes of damages in clay core rockfill (CCR) dams is the deterioration of the rockfill material over time and big settlements in the dam body. Therefore, the forecast of the settlements and principal stresses in a CCR dam is extremely important for the safety and future of these important water structures. In this study, changes in the nonlinear behavior of a CCR dam were examined by effects of the various reservoir water heights. Moreover, the geodetic measurements were confirmed with the nonlinear analysis results. Atatürk Dam, which is the largest CCR dam in Turkey, was selected for three-dimensional (3D) nonlinear analyses. First, a 3D finite-difference model of Atatürk Dam was created using the FLAC3D software, which is based on the finite-difference method. A Mohr-Coulomb material model was used for the dam body materials (e.g., clay core, filters, alluvium, rockfill) and foundation for the 3D numerical analyses. Numerical analyses were carried out for five various reservoir water heights: empty reservoir, 50, 100, 153, and 170 m (full reservoir). According to the finite-difference analyses, the effect of various reservoir water heights on the nonlinear behavior of the Atatürk dam was assessed in detail, and how much maximum vertical settlement will occur in the Atatürk Dam body in the future was determined. In addition, principal stresses and horizontal displacements were evaluated for each reservoir condition, and these results were compared with each other. This study demonstrated that as the reservoir water height increased at the upstream side of the dam, the principal stresses and vertical-horizontal deformations occurring in the dam body obviously changed and increased. In the second part of this study, the geodetic vertical settlement results observed by the General Directorate of State Hydraulic Works (DSI) between 1992 and 2013 were presented graphically. These geodetic observation results and numerical analyses were compared in detail, and the geodetic measurement results were confirmed by numerical analysis results.
 
Division of a 3D sliding mass into columns 
Characteristics of Soil Mass for Different Case Studies
Safety Factors for Different Cases Studies
(a) 3D wedge-shaped sliding surface (Case A); (b) 3D view of wedge-shaped sliding surface; (c) 3D wedge-shaped sliding surface (with water pressure) (Case B); (d) 3D wedge-shaped sliding surface; (e) 3D wedge-shaped sliding surface; (f) changing gradient of sliding surface of Case A (Case E); (g) changing lateral gradient of sliding surface of Case A (Case F); (h) 3D wedge-shaped sliding surface (Case G); (i) forces acting on a divided column adding a horizontal force; (j) 3D wedge-shaped sliding surface (Case H) 
( Continued ). 
Article
An assessment of three-dimensional slope stability analysis methods in terms of safety factors using several idealized sliding masses composed of plane sliding surfaces was made. Three-dimensional safety factors were calculated and compared for different study cases considered in this study on the basis of the exact solution methods, the Hovland method, and the 3D simplified Janbu method. Parameters investigated in this study included the effect of water pressure, horizontal seismic force, the changing gradient of a sliding surface, the changing lateral gradient of a sliding surface, and anchor force. Results showed that the Hovland method gives smaller safety factor values compared to the exact solutions, especially in cases of narrow failure width and high water pressure along sliding surfaces whereas the 3D simplified Janbu method gives the same safety factor values as the exact solutions. (C) 2012 American Society of Civil Engineers.
 
Article
The evaluation of the state of stress in a backfilled stope is necessary for assessing the stability of the sides and assisting in barricade design. To date, a few analytical models have been proposed in the literature for the estimation of the earth pressures of fill material; however, these models do not consider the three-dimensional (3D) inclined-stope geometry or consolidation of the material in a passive state. In this paper, an analytical model is proposed for the estimation of earth pressures by considering pore-water pressure and the consolidation effect of the fill material for different state conditions in an inclined 3D stope. The proposed model was validated with experimental works and another analytical model. The geotechnical properties of cemented backfill material were determined as the key inputs for this model. The model was applied to estimate the vertical and horizontal stresses that may develop in a filled stope with length, width, and height of 40, 20, and 60 m, respectively, and is inclined at 75° from the horizontal. This information is useful for designing the thickness of a barricade during a filling operation.
 
Article
Because of the heterogeneous layered characteristics of geomaterials, analysis of tunnel stability may be complicated, and such characteristics increase the possibility of progressive failure of the surrounding rock banks. This paper offers an analytical upper-bound approach to the analysis of the progressive collapse of deep rectangular tunnels based on three-dimensional (3D) velocity discontinuity surfaces. A symmetric 3D rotational progressive failure mechanism that considers the presence of rock layers partly induced by weathering is initially proposed and analyzed with the upper-bound theorem. In this approach, the range and shape of potential falling blocks are determined with use of the variational principle and the partition optimization method. The results obtained with the proposed approach showed good agreement and consistency with existing literature. Sensitivity analysis was also conducted to assess the effects of relevant parameters on the scope of impending blocks. Such analysis can also shed light on the collapse mechanism at failure and can be applied to projects under stratified or deteriorated rock masses, areas in which studies are limited at present.
 
Article
Three-dimensional (3D) complete nonlinear methods for examining soil–building interaction based on an input seismic wavefield were developed. A seismic wavefield means seismic waves propagating in a 3D medium. Vertical ground motions and the material nonlinearity of the superstructure and the piles were incorporated into earlier methods. Consequently, employing a three-component input wavefield including surface waves, the methods are able to treat nonlinear behavior of the superstructure and the piles in the cases of soils with nonlinear and liquefaction behavior. The feasibility of the methods was demonstrated using a midrise RC building in the lakebed zone of Mexico City and a midrise RC building and a wood building in the reclaimed zone of Tokyo Bay. The response of a midrise RC building of Tokyo was displayed. The methods provide reasonable nonlinear building performance. Building responses became excessively large following extremely large increases in the amplitudes of surface waves in liquefied soils, thereby successfully indicating that Japanese RC building damage concentrates in the first story.
 
Article
The analysis of the geometry of porous media is an important aspect of modern soil sciences. This comes from the fact that not only experimental studies but also numerical simulations demand a considerable knowledge of the porous matrix involved. Subsequently, the combination of microtomography, three-dimensional (3D) printing, and numerical simulations is studied. The first step in this process is choosing an artificial model for the soil. In the present study, 3D cellular automata were chosen. Following that, pore-scale permeability numerical simulations were considered in such artificial porous media. To bring numerical simulations to real-world situations, artificial porous media were 3D printed. By means of the methodology hereby presented, it is possible to generate specific porous media to isolate and study a given phenomenon of interest. The printings were subjected to a metrological analysis, which revealed that, for all samples analyzed, more than 95% of the linear deviations between the print and the computational model were smaller than the resolution of the printer (0.3 mm). This validates the usage of 3D prints as valuable tools to build artificial porous media. The real permeabilities of the printed porous media were obtained by a permeability experiment. Finally, numerical and real permeability values were compared, and a scale analysis for this property was carried out. It was found that the numerical routines can be used to correctly estimate the real permeability of a given porous medium. For example, the shape of the pore space can be completely known by digitally analyzing the computational medium, and specific parameters (e.g., pore throat size, pore size distribution, hydraulic mean radius, tortuosity) can be explicitly related to its permeability. In contrast, other 3D printing techniques have to be considered. Printing in flexible materials, for example, could provide samples for consolidation analyses.
 
Article
The kinematical approach of limit analysis has been historically employed to assess slope stability in the geotechnical community, for which most three-dimensional (3D) failure mechanisms are generally based on a composite of multiple common geometrical bodies. Although these failure mechanisms are straightforward, they may not perform well for slopes that involve multilayered soils with heterogeneous shear strength parameters. This paper aims at proposing a new 3D failure mechanism for steep slopes using a spatial discretization technique. The proposed failure mechanism is composed of a large number of elemental blocks that are generated point by point obeying the kinematically admissible velocity field and the normality condition. The discretization scheme makes it possible to simplify the calculations of internal energy dissipations and external work rates on the failure mechanism when both the soil properties and external loadings are spatially changing. The performance of the proposed method is illustrated to examine the stability of steep slopes in homogeneous soils, multilayer soils, and spatially variable soils, showing good agreements with previously published results and numerical modelings.
 
Article
The aim of this study is to propose an effective approach to evaluate the stability of a shield tunnel face with tensile strength cutoff by using the upper-bound limit analysis method. Based on the discretization and "point by point"techniques, two improved rotational failure mechanisms, namely the improved collapse failure mechanism and the improved blowout failure mechanism, are developed with the tensile cutoff for the first time. Based on these improved failure mechanisms, the critical collapse and blowout pressures of tunnel faces are then determined by using the upper-bound limit analysis method. The proposed method is then validated by comparisons with previous analytical solutions and numerical results, showing that the proposed method is an effective approach to evaluate the stability of shield tunnel faces. The influences of model parameters on the critical support pressures and the failure feature of the proposed mechanisms are finally presented.
 
Top-cited authors
B. Indraratna
  • University of Technology Sydney
Cholachat Rujikiatkamjorn
  • University of Technology Sydney
Mark Randolph
  • University of Western Australia
Nasser Khalili
  • UNSW Sydney
Behzad Fatahi
  • University of Technology Sydney