Geomechanical Problems Research Articles

Modelling suction instabilities in soils at varying degrees of saturation

Wetting paths imparted by the natural environment and/or human activities affect the state of soils in the near-surface, promoting transitions across different regimes of saturation. This paper discusses a set of techniques aimed at quantifying the role of hydrologic processes on the hydro-mechanical stability of soil specimens subjected to saturation events. Emphasis is given to the mechanical conditions leading to coupled flow/deformation instabilities. For this purpose, energy balance arguments for three-phase systems are used to derive second-order work expressions applicable to various regimes of saturation. Controllability analyses are then performed to relate such work input with constitutive singularities that reflect the loss of strength under coupled and/or uncoupled hydro-mechanical forcing. A suction-dependent plastic model is finally used to track the evolution of stability conditions in samples subjected to wetting, thus quantifying the growth of the potential for coupled failure modes upon increasing degree of saturation. These findings are eventually linked with the properties of the field equations that govern pore pressure transients, thus disclosing a conceptual link between the onset of coupled hydro-mechanical failures and the evolution of suction with time. Such results point out that mathematical instabilities caused by a non-linear suction dependent behaviour play an important role in the advanced constitutive and/or numerical tools that are commonly used for the analysis of geomechanical problems in the unsaturated zone, and further stress that the relation between suction transients and soil deformations is a key factor for the interpretation of runaway failures caused by intense saturation events.

Multiscale insights into classical geomechanics problems

SummaryWe pay a revisit to some classical geomechanics problems using a novel computational multiscale modelling approach. The multiscale approach employs a hierarchical coupling of the finite element method (FEM) and the discrete element method. It solves a boundary value problem at the continuum scale by FEM and derives the material point response from the discrete element method simulation attached to each Gauss point of the FEM mesh. The multiscale modelling framework not only helps successfully bypass phenomenological constitutive assumptions as required in conventional modelling approaches but also facilitates effective cross‐scale interpretation and understanding of soil behaviour. We examine the classical retaining wall and footing problems by this method and demonstrate that the simulating results can be well validated and verified by their analytical solutions. Furthermore, the study sheds novel multiscale insights into these classical problems and offers a new tool for geotechnical engineers to design and analyse geotechnical applications based directly upon particle‐level information of soils. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical modeling of rock fracture and fragmentation under impact loading using discrete element method

The fracture and fragmentation of rock materials are basic and important problem in geomechanics and blasting engineering. An approach, which can simulate the process of fracture and fragmentation of rock materials, is introduced in this work. A beam–particle model is first introduced in the frame of the discrete element method. In the beam–particle model, the neighboring elements are connected by beams. Consequently, a beam network is formed in the particle system. The strength characteristics of rock materials are reflected by the beam network. The strength criterion was then built to verify whether a beam exists or not. The process of rock fracture and fragmentation is described by the gradual disappearance of beams. Finally, two cases were presented to indicate the validity of the method proposed in this work.

Application of a GPU-accelerated hybrid preconditioned conjugate gradient approach for large 3D problems in computational geomechanics

This paper presents a hybrid preconditioning technique for Conjugate Gradient method and discusses its parallel implementation on Graphic Processing Unit (GPU) for solving large sparse linear systems arising from application of interior point methods to conic optimization problems in the context of nonlinear Finite Element Limit Analysis (FELA) for computational Geomechanics. For large 3D problems, the use of direct solvers in general becomes prohibitively expensive due to exponentially growing memory requirements and computational time. Besides, the so-called saddle-point systems resulting from use of optimization framework is not an exemption. On the other hand, although preconditioned iterative methods have moderate storage requirements and therefore can be applied to much larger problems than direct methods, they usually exhibit high number of iterations to reach convergence. In present paper, we show that this problem can be effectively tackled using the proposed hybrid preconditioner along with an elaborate implementation on GPU. Furthermore, numerical results verify the robustness and efficiency of the proposed technique.

A Timoshenko finite element straight beam with internal degrees of freedom

SummaryWe present hereafter the formulation of a Timoshenko finite element straight beam with internal degrees of freedom, suitable for nonlinear material problems in geomechanics (e.g., beam type structures and deep pile foundations). Cubic shape functions are used for the transverse displacements and quadratic for the rotations. The element is free of shear locking, and we prove that one element is able to predict the exact tip displacements for any complex distributed loadings and any suitable boundary conditions. After the presentation of the virtual power and the weak form formulations, the construction of the elementary stiffness matrix is detailed. The analytical results of the static condensation method are provided. It is also proven that the element introduced by Friedman and Kosmatka in , with shape functions depending on material properties, is derived from the new beam element. Validation is provided using linear and material nonlinear applications (reinforced concrete column under cyclic loading) in the context of a multifiber beam formulation. Copyright © 2015 John Wiley & Sons, Ltd.

An ALE method for penetration into sand utilizing optimization-based mesh motion

The numerical simulation of penetration into sand is one of the most challenging problems in computational geomechanics. The paper presents an arbitrary Lagrangian–Eulerian (ALE) finite element method for plane and axisymmetric quasi-static penetration into sand which overcomes the problems associated with the classical approaches. An operator-split is applied which breaks up solution of the governing equations over a time step into a Lagrangian step, a mesh motion step, and a transport step. A unique feature of the ALE method is an advanced hypoplastic rate constitutive equation to realistically predict stress and density changes within the material even at large deformations. In addition, an efficient optimization-based algorithm has been implemented to smooth out the non-convexly distorted mesh regions that occur below a penetrator. Applications to shallow penetration and pile penetration are given which make use of the developments.

A Mathematical Investigation of the Temperature Dependence of Effective Compressibility of Saturated Shales

A Mathematical Investigation of the Temperature Dependence of Effective Compressibility of Saturated Shales Carbon geosequestration initiative is an infant environmental remediation approach that is universally acceptable but lacks experience when it comes to predicting the fate of the storage gas. Consequently, one way to predict the evolution of the storage system with regard to subsurface gas migration and attendant Geomechanical problems is to seismically monitor the injection project as found in the Sleipner gas field injection in the Norwegian sector of the North Sea.

A sequential-adaptive strategy in space–time with application to consolidation of porous media

Issues related to space-time adaptivity for a class of nonlinear and time-dependent problems are discussed. The dG(k)-methods are adopted for the time integration, and the a posteriori error control is based on the appropriate dual problem in space-time. One key ingredient is to decouple the error generation in space and time with a hierarchical decomposition of the discrete space of dual solutions. The main idea put forward in the paper is to increase the computational efficiency of the adaptive scheme by avoiding recursive adaptations of the whole time-mesh; rather, the space-mesh and the time-step defining each finite space-time slab are defined in a truly sequential fashion. The proposed adaptive strategy is applied to the coupled consolidation problem in geomechanics involving large deformations. Its performance is investigated with the aid of a numerical example in 2D.

Semi-Lagrangian reproducing kernel particle method for slope stability analysis and post-failure simulation

Slope stability analyses are often performed using Limit Equilibrium Methods (LEMs) and Finite Element Method (FEM). However, these methods can only model the slope condition up to the point of failure. Meshfree methods, which do not require a mesh or a grid in the simulation process, have the potential to model the post-failure slope behavior as mesh tangling would not occur to cause numerical instability and non-convergence. Hence, while retaining the benefits of conventional numerical schemes, meshfree method can be more advantageous when problems with large deformation are encountered. In this paper, Semi-Lagrangian Reproducing Kernel Particle Method (SLRKPM), which is a type of meshfree method, is extended to analyze geomechanics problems such as the stability of a slope and post failure slope behavior. The results from SLRKPM agree well with those from convention methods (LEMs and FEM) in terms of factor-of-safety and failure surface. In addition, SLRKPM is able to simulate the slope failure process and successfully capture the development of shear band. This proves that SLRKPM has a significant advantage over FEM when dealing with problems involving large deformation and failure of geomaterials.

Efficiency of High-Order Elements in Large-Deformation Problems of Geomechanics

AbstractThis paper investigates the application of high-order elements within the framework of the arbitrary Lagrangian-Eulerian method for the analysis of elastoplastic problems involving large deformations. The governing equations of the method as well as its important aspects such as the nodal stress recovery and the remapping of state variables are discussed. The efficiency and accuracy of 6-, 10-, 15-, and 21-noded triangular elements are compared for the analysis of two geotechnical engineering problems, namely, the behavior of an undrained layer of soil under a strip footing subjected to large deformations and the soil behavior in a biaxial test. The use of high-order elements is shown to increase the accuracy of the numerical results and to significantly decrease the computational time required to achieve a specific level of accuracy. For problems considered in this study, the 21-noded elements outperform other triangular elements.

A parallel linear solver exploiting the physical properties of the underlying mechanical problem

The iterative solution of large systems of equations may benefit from parallel processing. However, using a straight-forward domain decomposition in “layered” geomechanical finite element models with significantly different stiffnesses may lead to slow or non-converging solutions. Physics-based domain decomposition is the answer to such problems, as explained in this paper and demonstrated on the basis of a few examples. Together with a two-level preconditioner comprising an additive Schwarz preconditioner that operates on the sub-domain level, an algebraic coarse grid preconditioner that operates on the global level, and additional load balancing measures, the described solver provides an efficient and robust solution of large systems of equations. Although the solver has been developed primarily for geomechanical problems, the ideas are applicable to the solution of other physical problems involving large differences in material properties.

Typical geomechanical problems associated with railroads on shrink-swell soils

Problems associated with continuous settlement are typically observed in railroads in Texas. Different physical mechanisms can be behind these issues. Natural soils in Texas are dominated by shrink-swell clays (also known as expansive soils). These kinds of clays are characterized by significant expansions and contractions when they are subjected to wetting and drying processes, respectively. Railways on shrink-swell soils are subjected to huge solicitations associated with the volume changes of the soil, generally leading to unacceptable uneven settlements. Relative movements of railroads constructed on this type of soil can also be related to progressive shear failure, and long term consolidation and creep. Uneven settlements affect both: operational costs and safety. The mechanisms behind the observed railroads problems on shrink-swell soils, and the associated (possible) remedial solutions, are still unclear. A site in Texas has been recently selected to study in detail the aforementioned problems. The case study consists of three different sections: a fill, a cut, and a reference section. In this paper we discuss the typical geomechanical problems associated with railroads in Texas, Some possible remedial solutions for those problems are discussed as well. We also present the test site selected to study this problem under actual conditions and at full scale. Numerical analyses involving a typical railroad section are presented and discussed in this paper as well.

Isogeometric Boundary Element Method for the Simulation in Tunneling

Isogeometricfiniteelement methods and more recentlyboundaryelement methods have been successfully applied to problems in mechanical engineering and have led to an increased accuracy and a reduction in simulation effort. Isogeometric boundary element methods have great potential for the simulation of problems in geomechanics, especially tunneling because an infinite domain can be considered without truncation. In this paper we discuss the implementation of the method in the research software BEFE++. Based on an example of a spherical excavation we show that a significant reduction in the number of parameters for describing the excavation boundary as well as an improved quality of the results can be obtained.

Accounting for depth-wise linear change of stresses in the intact rock mass in geomechanical problems

The authors discuss formulation of boundary conditions in problems on stress-strain state of rocks around an underground excavation. The classical formulations neglect the presupposition of linearity of stress field in an intact rock mass with depth and disregard the discrepancy of the calculated and actual behavior of rocks. The presented study is based on the linearity of initial stresses and the computational domain boundary conditions that assume stress linearity and unaltered boundary conditions during drivage. The problem on stress-strain state is divided into two problems due to option of formulating accurately boundary conditions for the horizontal boundary and the absence of such option for the vertical boundary.

Multiphysics implementation of advanced soil mechanics models

Using multiphysics computer codes has become a useful tool to solve systems of partial differential equations. However, these codes do not always allow for the free introduction of implicitly defined state functions when automatic differentiation is used to compute the iteration matrix. This makes it considerably more difficult to solve geomechanical problems using non-linear constitutive models. This paper proposes a method for overcoming this difficulty based on multiphysics capabilities. The implementation of the well-known Barcelona basic model is described to illustrate the application of the method. For this purpose, without including formulation details addressed by other authors, the fundamentals of its implementation in a finite element code are described. Examples that demonstrate the scope of the proposed methodology are also presented.

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

Accuracy of dynamic disk-based DDA with respect to a single sliding disk cluster

Disk clusters are developed to represent the shape of granular materials more precisely (compared to circular particles) and to minimise excessive rolling. Investigating the behaviour of dynamic disk-based discontinuous deformation analysis (DDA) with disk clusters is very important to evaluate the applicability of disk-based DDA to dynamic problems in geomechanics. In this paper, the accuracy of disk-based DDA under dynamic conditions is studied by a comprehensive sensitivity analysis. The results obtained by disk-based DDA are compared with the analytical solutions of a disk cluster on an incline subjected to gravitational force only, and three different accelerations of increasing complexity with sinusoidal input functions as well as gravitational load. In this research, the effects of time step size and interface friction angles on the results are studied. Overall, most of the error for both velocity and displacement occurs at the beginning of the solution. With increasing friction angle, the initial perturbation of the solution increases in the case of sliding under gravitational force only, and decreases in the case of sliding under dynamic loads. This study shows that disk-based DDA predicts accurately the velocities and displacements derived with respect to the frictional resistance offered by the inclines.

Large deformation dynamic analysis of saturated porous media with applications to penetration problems

This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.

Post-peak failure modulus in problems of mining geo-mechanics

This paper presents one of the geo-mechanical parameters — post-peak failure modulus. It is a parameter of great importance in solving various problems of mining geo-mechanics at the current level of experimental knowledge. Post-peak failure modulus is obtained through examining rock samples which are loaded in a stiff servo-controlled testing machine. Construction of the machine and its parameters enable obtaining stress-strain characteristics the total strain range of the rock which occurs as a result of increasing load until it reaches the level of residual stress. The most important application of post-peak failure modulus in mining geo-mechanics is using it in estimating the destruction of rocks and rock mass, forecasting rock mass proneness to rock bursts and estimating rock burst hazard, determining the optimum pace of advance for mining activities considering induced seismicity and rock mass proneness to rock bursts, dimensioning pillars in room-and-pillar systems and determining failure zones around workings of various shapes.

삼차원 불연속면 연결구조 해석 및 가시화 소프트웨어 모듈 개발

본 연구는 삼차원 지질 모델링 소프트웨어 개발의 일환으로 불연속면의 구조기하형태에 대한 삼차원적 해석 및 가시화를 수행 할 수 있는 새로운 소프트웨어 모듈을 개발하는 데에 목적이 있다. 불연속면 연결구조의 삼차원 해석 및 가시화 알고리즘을 바탕으로 개발된 소프트웨어는 C++언어 기반의 MFC 및 OpenGL 라이브러리를 응용하여 Microsoft Visual Studio 상에서 제작되었다. 개발된 소프트웨어는 BOUNDARY, DISK3D, FNTWK3D, CSECT, BDM 등의 모듈을 포함하며 각각의 모듈은 해석영역 구성, 불연속면 네트워크 시스템의 가시화, 등가파이프의 산정, 단면도 작성, 시추공 자료 관리 등 절리성 암반의 삼차원 구조기하형태 해석에 관련된 다양한 기능을 수행한다. 이 연구에서 개발한 불연속면 연결구조의 삼차원 가시화 및 해석 소프트웨어는 불연속체 기반의 암반강도 및 변형성에 관한 연구, 수리지질학적 특성에 관한 연구 및 사면안정 연구를 수행함에 있어서 활용도가 높을 것으로 판단되며 국내 소프트웨어 산업의 경쟁력을 높이는데 기여할 수 있을 것으로 기대된다. As part of the development of the 3-D geologic modeling software, this study addresses on new development of software modules that can perform the analysis and visualization of the fracture network system in 3-D. The developed software modules, such as BOUNDARY, DISK3D, FNTWK3D, CSECT and BDM, are coded on Microsoft Visual Studio platform using the MFC and OpenGL library supported by C++ program language. Each module plays a role in construction of analysis domain, visualization of fracture geometry in 3-D, calculation of equivalent pipes, production of cross-section map and management of borehole data, respectively. The developed software modules for analysis and visualization of the 3-D fracture network system can be used to tackle the geomechanical problems related to strength, deformability and hydraulic behaviors of the fractured rock masses. All these benefits will further enhance the economic competitiveness of the domestic software industry.