Stability of earth slopes. Part I: two‐dimensional analysis in closed‐form

A closed‐form solution (CFS) satisfying both equilibrium of moments and forces for the stability analysis of earth slopes in 2D is proposed. The sliding surface is assumed circular and treated as a rigid body, allowing the internal state of stress to be ignored. The proposed solution can be applied to both homogenous and non‐homogenous slopes of either simple or complex geometry, and can also deal with any kind of additional loading. The method is based on the fact that, all possible forces acting on the slope can be projected onto the failure surface where they are broken into driving and resisting ones. Comparison of the safety factors obtained by the proposed CFS and those obtained by traditional limit equilibrium methods, as applied to several test examples, indicates that the proposed method is more conservative, whereas moreover, it gives a more realistic point of view for the formation of tension crack in slopes. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Modeling progressive failures in rock slopes with non‐persistent joints using the numerical manifold method

Rock slope failure is a complex process that usually involves both opening/sliding along pre‐existing discontinuities as well as fracturing of intact rock bridges. Discontinuity persistence is an important factor governing rock slope instabilities. However, traditional slope failure analysis assumes persistent discontinuities, and rock slope fails along a predefined persistent continuous potential failure surface because of the limitations of the analysis tools. This paper proposes the numerical manifold method (NMM) incorporated with a Mohr–Coulomb criterion‐based fracturing algorithm to simulate the progressive failure of rock slopes with non‐persistent joints. Detailed fracturing algorithm is first presented. Then, the NMM enabling fracturing is calibrated through simulating an edge‐cracked plate and the Brazilian test. Lastly, the developed code is applied to investigate the failure process of rock slopes involving non‐persistent joints. Numerical results indicate that the proposed method can capture the opening/sliding along existing discontinuities, the fracturing in intact rock bridges and the final kinematic release. Progressive slope failure is well exhibited. Copyright © 2013 John Wiley & Sons, Ltd.     

A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd.     

Implications of variationally derived 3D failure mechanism

This paper revisits the variational limit equilibrium (LE) analysis of three‐dimensional (3D) slope stability in the context of limit analysis (LA). It proves the kinematic admissibility of the 3D mechanism in LA, although it was derived from LE variational extremization. It also includes algorithms in the realm of LA that are associated with the variational mechanism. A comparison between the variational results and reported LA upper‐bound or LE closed‐form results is conducted. It demonstrates that the variationally derived mechanism consistently yields upper‐bound solutions for 3D symmetrical slopes that are as accurate as those produced by postulated mechanisms in LA. However, the results are more critical than those derived from spherical failure mechanism in LE. The generalized log spiral 3D mechanism rigorously legitimizes the variational slope stability analysis in both frameworks of mechanics LE and LA. Stability charts were produced where the 3D factor of safety can be assessed for a constrained length of failure, while including factors like pore water pressure and seismic loading. The results presented within this study demonstrate the capabilities of the variational 3D solution and can be used to evaluate approximate methods, numerical or closed‐form, developed in 3D slope stability analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Depositional model for lacustrine nearshore subaqueous fans in a rift basin: The Eocene Shahejie Formation,Dongying Sag,Bohai Bay Basin,China

The origin of the fourth member of the Eocene Shahejie Formation in the northern steep slopes of the Minfeng Sub‐sag, Dongying Sag, China, was investigated by integrating core studies and flume tank depositional simulations. A non‐channelized depositional model is proposed in this paper for nearshore subaqueous fans in steep fault‐controlled slopes of lacustrine rift basins. The deposits of nearshore subaqueous fans along the base of steep border‐fault slopes of rift basins are typically composed of deep‐water coarse‐grained sediment gravity‐flow deposits directly sourced from adjacent footwalls. Sedimentation processes of nearshore subaqueous fans respond to tectonic activities of boundary faults and to seasonal rainfall. During tectonically active stages, subaqueous debris flows triggered by episodic movements of border‐faults dominate the sedimentation. During tectonically quiescent stages, hyperpycnal flows generated by seasonal rainfall‐generated floods, normal discharges of mountain‐derived rivers and deep‐lacustrine suspension sedimentation are commonly present. The results of a series of flume tank depositional simulations show that the sediments deposited by subaqueous debris flows are wedge‐shaped and non‐channelized, whereas the sediments deposited by hyperpycnal flows generated by sporadic floods from seasonal rainfall are characterized by non‐channelized, coarse‐grained lobate depositional bodies which switch laterally because of compensation sedimentation of hyperpycanal flows. The hyperpycnal‐flow‐deposited non‐channelized lobate depositional bodies can be divided into a main body and lateral edges. The main body can be further subdivided into a proximal part, middle part and frontal part. Normal mountain‐derived river‐discharge‐deposited sediments are characterized by thin‐bedded, fine‐grained sandstones and siltstones with a limited distribution range. Normal mountain‐derived river‐discharge‐deposited sediments and deep‐lacustrine mudstones are commonly eroded in the area close to boundary faults. A nearshore subaqueous fan can be divided into three segments: inner fan, middle fan and outer fan. The inner fan is composed of debrites and the proximal part of the main body. The middle fan consists of the middle part of the main body and lateral edges, normal mountain‐derived river‐discharge‐deposited fine‐grained sediments and deep‐lacustrine mudstones. The outer fan comprises the frontal part of the main body, lateral edges, and deep‐lacustrine mudstones. Based on the non‐channelized depositional model for nearshore subaqueous fans, criteria for stratigraphic subdivision and correlation are discussed and applied.     

Numerical studies of shear banding in interface shear tests using a new strain calculation method

Strain localization is closely associated with the stress–strain behaviour of an interphase system subject to quasi‐static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two‐dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non‐linear stress–strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post‐peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8–10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd.     

Reinforcing mechanism of anchors in slopes: a numerical comparison of results of LEM and FEM

This paper reports the limitation of the conventional Bishop's simplified method to calculate the safety factor of slopes stabilized with anchors, and proposes a new approach to considering the reinforcing effect of anchors on the safety factor. The reinforcing effect of anchors can be explained using an additional shearing resistance on the slip surface. A three‐dimensional shear strength reduction finite element method (SSRFEM), where soil–anchor interactions were simulated by three‐dimensional zero‐thickness elasto‐plastic interface elements, was used to calculate the safety factor of slopes stabilized with anchors to verify the reinforcing mechanism of anchors. The results of SSRFEM were compared with those of the conventional and proposed approaches for Bishop's simplified method for various orientations, positions, and spacings of anchors, and shear strengths of soil–grouted body interfaces. For the safety factor, the proposed approach compared better with SSRFEM than the conventional approach. The additional shearing resistance can explain the influence of the orientation, position, and spacing of anchors, and the shear strength of soil–grouted body interfaces on the safety factor of slopes stabilized with anchors. Copyright © 2003 John Wiley & Sons, Ltd.     

A morphometric analysis of tunnel valleys in the eastern North Sea based on 3D seismic data

A 1250 km² 3D seismic volume is used to provide a detailed spatial and geometrical analysis of fifteen Pleistocene tunnel valleys in the Danish North Sea. All the valleys are buried; they are up to 39 km long, 3–4 km wide and up to 350 m deep. The valleys are part of a vast tunnel valley province covering an area of some 0.5 million km² of the formerly glaciated lowland areas of North West Europe. The valleys consist of non‐branching, non‐anastomosing troughs; they exhibit strongly undulating bottom profiles with numerous sub‐basins and thresholds, and are characterised by adverse end slopes. Cross‐cutting relationships and theoretical considerations suggest the occurrence of seven major episodes of valley incision attributed to ice marginal oscillations within a few glacials. Calculations considering the valley end gradients and theoretical ice‐surface profiles suggest that the valleys were formed by pressurised subglacial meltwater erosion. Given a range of theoretical ice‐surface profiles, the adverse end slopes are well beyond the supercooling threshold, which suggests that the water was not in thermal equilibrium with the basal ice and that flow was concentrated in substantial conduits with sufficient mass and flux to maintain water temperature well above the freezing point. Copyright © 2007 John Wiley & Sons, Ltd.     

Visualization of material stiffness in geomechanics analysis

This paper presents novel visualization techniques to simplify representation of the fourth‐order material stiffness tensor as a set of three‐dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non‐linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three‐dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non‐linear and path dependent material models. The proposed stiffness visualization can be represented as 3‐D, 2‐D and 1‐D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic response of slopes subjected to incident SV wave by an improved boundary element approach

In this paper, an improved boundary element approach for 2D elastodynamics in time‐domain is presented. This approach consists in the truncation of time integrations, based on the rapid decrease of the fundamental solutions with time. It is shown that an important reduction of the computation time as well as the storage requirement can be achieved. Moreover, for half‐plane problems, the size of boundary element (BE) meshes and the computation time can be significantly reduced. The proposed approach is used to study the seismic response of slopes subjected to incident SV waves. It is found that large amplifications take place on the upper surface close to the slope, while attenuations are produced on the lower surface. The results also show that surface motions become very complex when the incident wavelength is comparable with the size of the slope or when the slope is steep. Copyright © 2006 John Wiley & Sons, Ltd.     

A finite strain closed‐form solution for the elastoplastic ground response curve in tunnelling

The ground response to tunnel excavation is usually described in terms of the characteristic line of the ground (also called ‘ground response curve’, GRC), which relates the support pressure to the displacement of the tunnel wall. Under heavily squeezing conditions, very large convergences may take place, sometimes exceeding 10–20% of the excavated tunnel radius, whereas most of the existing formulations for the GRC are based on the infinitesimal deformation theory. This paper presents an exact closed‐form analytical solution for the ground response around cylindrical and spherical openings unloaded from isotropic and uniform stress states, incorporating finite deformations and linearly elastic‐perfectly plastic rock behaviour obeying the Mohr–Coulomb failure criterion with a non‐associated flow rule. Additionally, the influence of out‐of‐plane stress in the case of cylindrical cavities under plane‐strain conditions is examined. The solution is presented in the form of dimensionless design charts covering the practically relevant parameter range. Finally, an application example is included with reference to a section of the Gotthard Base tunnel crossing heavily squeezing ground. The expressions derived can be used for preliminary convergence assessments and as valuable benchmarks for finite strain numerical analyses. Copyright © 2014 John Wiley & Sons, Ltd.     

高温冻土区新型复合护坡降温机制研究

遮阳板碎石复合护坡是一种集碎石护坡和遮阳板护坡双重效用于一体的新型复合护坡结构,是一种很好的治理高温冻土区块碎石护坡路基病害的补强措施。基于遮阳板和块碎石单个工程措施降温机制的研究,通过对这种新型复合护坡路基的温度场和速度场特征以及降温过程的研究,提出新型复合护坡路基的降温机制。研究发现,封闭新型复合护坡的主要降温机制是：复合护坡中遮阳板有遮阳和挡风雪作用,碎石层有“热半导体”效应和“热屏蔽效应”（屏蔽遮阳板的二次辐射）;开放新型复合护坡的主要降温机制是：遮阳板有遮阳、挡风雪作用,碎石护坡有 “热屏蔽效应”（屏蔽热风和二次辐射）和“烟囱效应”,遮阳板和碎石护坡组合的通道有“虹吸效应”、“狭管效应”和 “烟囱效应”。研究成果完善和深化了新型复合护坡路基研究基础,而且对遮阳板和块碎石结构在青藏铁路或青藏公路中的应用提供科学依据和技术支撑。     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

Neural network prediction of the reliability of heterogeneous cohesive slopes

The reliability of heterogeneous slopes can be evaluated using a wide range of available probabilistic methods. One of these methods is the random finite element method (RFEM), which combines random field theory with the non‐linear elasto‐plastic finite element slope stability analysis method. The RFEM computes the probability of failure of a slope using the Monte Carlo simulation process. The major drawback of this approach is the intensive computational time required, mainly due to the finite element analysis and the Monte Carlo simulation process. Therefore, a simplified model or solution, which can bypass the computationally intensive and time‐consuming numerical analyses, is desirable. The present study investigates the feasibility of using artificial neural networks (ANNs) to develop such a simplified model. ANNs are well known for their strong capability in mapping the input and output relationship of complex non‐linear systems. The RFEM is used to generate possible solutions and to establish a large database that is used to develop and verify the ANN model. In this paper, multi‐layer perceptrons, which are trained with the back‐propagation algorithm, are used. The results of various performance measures indicate that the developed ANN model has a high degree of accuracy in predicting the reliability of heterogeneous slopes. The developed ANN model is then transformed into relatively simple formulae for direct application in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of the free surface flow of water–kaolinite mixture by moving particle semi‐implicit (MPS) method

The flow of water–kaolinite mixtures exhibits a non‐Newtonian nature that differs from the flow of Newtonian fluid. The varying viscosities and shear history of non‐Newtonian fluid flows necessitate the use of a rheology model in moving particle semi‐implicit (MPS) for the numerical studies. On the other hand, the Lagrangian method has the advantage of handling free surface flows with large deformation and fragmentation. This study proposes a mesh‐free Lagrangian method, namely, the MPS method, together with a simple rheology model to investigate the non‐Newtonian free surface flows. The rheological parameters required in the rheology model are determined based upon experiments. The proposed method is applied to a water–kaolinite mixture collapse problem and is proved to be capable of reproducing the significant flow features observed in laboratory experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Upper bound limit analysis using linear finite elements and non‐linear programming

A new method for computing rigorous upper bounds on the limit loads for one‐, two‐ and three‐dimensional continua is described. The formulation is based on linear finite elements, permits kinematically admissible velocity discontinuities at all interelement boundaries, and furnishes a kinematically admissible velocity field by solving a non‐linear programming problem. In the latter, the objective function corresponds to the dissipated power (which is minimized) and the unknowns are subject to linear equality constraints as well as linear and non‐linear inequality constraints. Provided the yield surface is convex, the optimization problem generated by the upper bound method is also convex and can be solved efficiently by applying a two‐stage, quasi‐Newton scheme to the corresponding Kuhn–Tucker optimality conditions. A key advantage of this strategy is that its iteration count is largely independent of the mesh size. Since the formulation permits non‐linear constraints on the unknowns, no linearization of the yield surface is necessary and the modelling of three‐dimensional geometries presents no special difficulties. The utility of the proposed upper bound method is illustrated by applying it to a number of two‐ and three‐dimensional boundary value problems. For a variety of two‐dimensional cases, the new scheme is up to two orders of magnitude faster than an equivalent linear programming scheme which uses yield surface linearization. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.