Finite element analysis of progressive failure in long slopes

Progressive failure in long natural clay slopes with an underlying weak shear zone is studied. The clay slope is assumed to be elastic–perfectly plastic, whereas the shear zone may have an elastic–plastic strain softening behaviour. The failure will occur due to the development of large shear deformations in the weak zone. The general behaviour, including the possibility of progressive failure, can be studied by the use of a one-dimensional finite element model. Other interesting matters which can be studied are critical load, critical disturbance and critical length of the slope. Numerical examples show the overall behaviour due to different residual shear strengths of the weak layer, end disturbance or change of pore pressure in the weak layer. Although simple, the proposed finite element model provides a practically applicable tool for the prediction of whether progressive failure will occur and in which manner the local failure will propagate.     

Finite element modelling of rock-socketed piles

Rock socketed piles have a number of features which differentiate them from other types of piles. The generally stubby geometry leads to more even distribution of capacity between shaft and base. However, the low ratio of pile modulus to rock modulus leads to high compressibility and this, coupled with a tendency for the load transfer response along the shaft to exhibit strain-softening, gives rise to an overall response where the shaft capacity may be fully mobilized, and potentially degraded, before significant mobilization of base load. The paper presents results of finite element analyses of the response of rock-socketed piles, with particular attention to the shaft response with and without intimate base contact. The shaft interface uses a model, developed from principles of tribology, that includes dilation (and strain-hardening) prior to peak shaft friction, followed by strain-softening at larger displacements. The results of the study are shown to be consistent with field measurements, and to capture effects of the absolute pile diameter on the peak shaft friction. It is also shown that intimate base contact mitigates significantly the degree of strain-softening of the shaft response.     

有限元法在滑坡稳定性分析中的应用

对比了滑坡稳定性分析的极限平衡法、数值分析法、概率法。而后,介绍了有限元法滑坡稳定性分析基本原理,并应用有限元法对中里滑坡进行了稳定性分析,得出了中里滑坡的主应力图和稳定系数,并将稳定系数与其他方法的结果进行了比较,得出有限元法是一种可靠的分析方法,其结果可应用于后期治理设计。      

Finite element modelling of rate-dependent ratcheting in granular materials

The present paper introduces a comprehensive model that is capable of describing the behaviour, under cyclic loading, of the granular materials used in railway tracks and road pavement. Its main thrust is the introduction of the “Chicago” law in a continuum approach to account for the ratcheting effects. It also emphasizes rate-dependency as a dissipative mechanism that acts independently or jointly with the ratcheting effect as well as the non-associated plasticity. The numerical procedure is based on the return mapping algorithm, where Newton’s method is used to calculate the nonlinear consistency parameter of the flow rule and to obtain a consistent tangent modulus. The model was applied to specific numerical examples including multi-axial and cyclic loading conditions.     

边坡大变形弹塑性有限元分析[Ⅱ]

本文应用Ｕｐｄａｔｅｄ Ｌａｇｒａｎｇｉａｎ有限元分析理论,分析了石龙庙滑坡的稳定性,其中包括滑坡的大变形,初始应力和超孔隙水压力。根据土的工程地质性质,滑坡体分为四层,土层被视为是弹塑性的,土的塑性屈服采用Ｄｒｕｃｋｅｒ－Ｐｒａｇｅｒ理想塑性屈服准则,挡土墙建成前后的滑坡应力和变形被分别分析和讨论,最后根据这些分析结果,提出了滑坡的整治方案。     

Finite element modelling of frictional instability between deformable rocks

Earthquakes are recognized as resulting from a stick–slip frictional instability along faults. Based on the node‐to‐point contact element strategy (an arbitrarily shaped contact element strategy applied with the static‐explicit algorithm for modelling non‐linear frictional contact problems proposed by authors), a finite element code for modelling the 3‐D non‐linear friction contact between deformable bodies has been developed and extended here to analyse the non‐linear stick–slip frictional instability between deformable rocks with a rate‐ and state‐dependent friction law. A typical fault bend model is taken as an application example to be analysed here. The variations of the normal contact force, the frictional force, the transition of stick–slip instable state and the related relative slip velocity along the fault between the deformable rocks and the stress evolution in the total bodies during the different stages are investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the non‐linear frictional instability between deformable rocks. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite element modelling of pressuremeter tests and footings on frozen soils

A finite element code is developed to model the structure-frozen soil/ice interaction using a time incrementing, fully implicit, iterative algorithm, and a constitutive model based on the concept that total strain tensor consists of an elastic and a creep component. The code is used to investigate the applicability and limitations of the power law as the creep model for frozen soil by simulating two pressuremeter tests. Two extended phenomenological models based on the generalized power law are used in axisymmetric finite element analyses to simulate two, long-term, stage-loaded pressuremeter tests, and comparison of results with test data indicates that one model demonstrates a better ability to approximate the actual response to subsequent load steps, under certain restrictions. Stress analyses demonstrate the ability of the constitutive model to show transient as well as subsequent quasi-stationary stress stages in creep analysis. Additional simulations of short-term pressuremeter tests on ice are performed to further illustrate some limitations of the power-law model. Examples for prediction of creep settlements on frozen geomaterials are demonstrated by considering the interaction of fully flexible circular footings and concrete cylindrical footings (of different embedment depths) with frozen sands.     

Finite element modelling of three-phase flow in deforming saturated oil reservoirs

A numerical simulation is presented for three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation systen which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous medium. An elastoplastic soil model, based on a Mohr–Coulomb yield surface, is used. The finite element method is applied to obtain simultaneous solutions to the governing equations where displacement and fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. The developed model is used to investigate the problems of three-phase fluid flow in a deforming saturated oil reservoir.     

Finite element modelling of transport of organic chemicals through soils

Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.     

Implementing landslide path dependency in landslide susceptibility modelling

Landslide susceptibility modelling—a crucial step towards the assessment of landslide hazard and risk—has hitherto not included the local, transient effects of previous landslides on susceptibility. In this contribution, we implement such transient effects, which we term “landslide path dependency”, for the first time. Two landslide path dependency variables are used to characterise transient effects: a variable reflecting how likely it is that an earlier landslide will have a follow-up landslide and a variable reflecting the decay of transient effects over time. These two landslide path dependency variables are considered in addition to a large set of conditioning attributes conventionally used in landslide susceptibility. Three logistic regression models were trained and tested fitted to landslide occurrence data from a multi-temporal landslide inventory: (1) a model with only conventional variables, (2) a model with conventional plus landslide path dependency variables, and (3) a model with only landslide path dependency variables. We compare the model performances, differences in the number, coefficient and significance of the selected variables, and the differences in the resulting susceptibility maps. Although the landslide path dependency variables are highly significant and have impacts on the importance of other variables, the performance of the models and the susceptibility maps do not substantially differ between conventional and conventional plus path dependent models. The path dependent landslide susceptibility model, with only two explanatory variables, has lower model performance, and differently patterned susceptibility map than the two other models. A simple landslide susceptibility model using only DEM-derived variables and landslide path dependency variables performs better than the path dependent landslide susceptibility model, and almost as well as the model with conventional plus landslide path dependency variables—while avoiding the need for hard-to-measure variables such as land use or lithology. Although the predictive power of landslide path dependency variables is lower than those of the most important conventional variables, our findings provide a clear incentive to further explore landslide path dependency effects and their potential role in landslide susceptibility modelling.     

川藏公路某滑坡抗滑桩工程效果的有限元后评价

在对川藏公路二郎山k2730段Ⅰ# 滑坡及其抗滑结构现场调研的基础上,依据预应力锚索抗滑桩中桩土相互作用特征引入接触单元,并改进了PCEP2D有限元软件,将滑坡和抗滑桩结构相互作用作为整体,对桩体位移、桩身弯矩、锚固段桩体接触单元应力分布做了分析。与传统计算方法、实际监测资料进行对比,结果表明,该滑坡治理工程效果较好。     

Evaluation of landslide triggering mechanisms in model fill slopes

Hong Kong is particularly susceptible to landslide risk due to the steep natural topography and prolonged periods of high intensity rainfall. Compounding the risk of slope failure is the existence of loose fill slopes which were constructed prior to the 1970s by end-tipping. A clear understanding of the underlying triggering mechanisms of fast landslides in fill slopes is required to analyse landslide risk and to optimise slope stabilisation strategies. The work described here had the objective of evaluating two candidate triggering mechanisms—static liquefaction and the transition from slide to flow due to localised transient pore water pressures—against observations of slope behaviour obtained from highly instrumented centrifuge model tests. These results indicate that static liquefaction is unlikely to occur if the model fill is unsaturated and the depth to bedrock large, as the high compressibility and mobility of air in the unsaturated void spaces allows the model fill slope to accommodate wetting collapse without initiating undrained failure. In contrast, high-speed failures with low-angle run-outs are shown to be easily triggered in model fill slopes from initially slow moving slips driven by localised transient pore water pressures arising from constricted seepage and material layering.     

Finite element modelling for evaluation of apparent resistivity over complex structures

The paper presents a computational algorithm designed for efficient modelling of apparent resistivity over complex geological structures, using finite element method. The algorithm can be used to study variations of apparent resistivities using any electrode configuration at any point on the earth’s surface, not necessarily regular. A Schlumberger apparent resistivity sounding curve over a buried anticline, is presented here as an example and compared with the corresponding analytical curve, to demonstrate the correctness of the FEM algorithm. The various potential derivatives required for the computation of apparent resistivities evaluated through different electrode configurations have been obtained by calculating the ‘influence coefficients’ using reciprocal theorems, an approach successfully applied in structural engineering. In essence, a set of self balancing nodal currents, obtained from the appropriate derivative(s) of the shape functions of the elements contributing to the point of observation, is applied as the load vector. The resulting quantities corresponding to the potential distribution in traditional finite element method, then, turn out to be the potential derivatives at the point of observation for different positions of the current electrodes. These are known as influence coefficients. The continuum nature of the domain beyond the region of interest has been modelled by using ‘infinite elements’ across which the potential is assumed to decay exponentially.     

Finite element modelling of ground surface displacements due to underground blasting

Elastic wave radiation from an equivalent cylindrical cavity due to an underground explosion is considered in detail. Both static and steady state dynamic finite element models are used to investigate the surface displacements due to the interaction of such wave radiation with both the free surface topography and stope formation. For a blast 430 m below the surface the models predict a negligible displacement effect due to the irregular topography but a significant effect due to the stope. A comparison between the models and a site experiment verified the cylindrical wave nature of the problem. Due to experimental uncertainties however it was difficult to clearly detect the surface displacement effect due to the large underground open stope.     

Ice, moraine, and landslide dams in mountainous terrain

We review recent work on ice, moraine, and landslide dams in mountainous terrain, thus complementing several comprehensive summaries on glacier dams in intracontinental and Arctic areas of low relief. We discuss the roles of tectonic and climatic forcing on ice-, moraine-, and landslide-dam formation and sudden drainage, and focus on similarities and differences between their geomorphic impacts on confined valleys drained by steep bedrock and gravel-bed rivers.Despite numerous reported failures of natural dams in mountain belts throughout the world, their relevance to long-term dynamics of mountain rivers remains poorly quantified. All types of dams exert local base-level controls, thus trapping incoming sediment and inhibiting fluvial bedrock incision. Pervasive geomorphic and sedimentary evidence of outburst events is preserved even in areas of high erosion rates, suggesting that sudden dam failures are characterized by processes of catastrophic valley-floor aggradation, active-channel widening, and downstream dispersion of sediment, during which little bedrock erosion seems to be achieved.We find that, in the absence of direct evidence of former dams, a number of similarities among the geomorphic and sedimentologic characteristics of catastrophic outburst flows may give rise to ambiguous inferences on the dam-forming process. This is especially the case for tectonically active mountain belts where there is ample and comparable potential for the formation and failure of ice, moraine, landslide, and polygenetic dams concomitant with climatic oscillations or earthquake disturbance. Hence, the palaeoclimatic implications of erroneously inferring the cause of dam formation may be significant.We recommend that future research on natural dams in mountainous terrain addresses (a) climate- and earthquake-controlled systematics in the pattern of formation and failure; (b) quantification of response of mountain rivers to catastrophic outburst events and their concomitant process sequences; (c) elaboration of a comprehensive classification of natural dams in mountainous terrain with special attention to polygenetic dams; (d) physical-based modelling of dam formation, failure, and routing of water and sediment outbursts; and (e) quantitative controls on the contribution of natural dams to sediment budgets in mountainous terrain.     

Magnetotelluric investigations for imaging electrical structure of Garhwal Himalayan corridor,Uttarakhand, India

Magnetotelluric investigations have been carried out in the Garhwal Himalayan corridor to delineate the electrical structure of the crust along a profile extending from Indo-Gangetic Plain to Higher Himalayan region in Uttarakhand, India. The profile passing through major Himalayan thrusts: Himalayan Frontal Thrust (HFF), Main Boundary Thrust (MBT) and Main Central Thrust (MCT), is nearly perpendicular to the regional geological strike. Data processing and impedance analysis indicate that out of 44 stations MT data recorded, only 27 stations data show in general, the validity of 2D assumption. The average geoelectric strike, N70°W, was estimated for the profile using tensor decomposition. 2D smooth geoelectrical model has been presented, which provides the electrical image of the shallow and deeper crustal structure. The major features of the model are (i) a low resistivity (<50Ωm), shallow feature interpreted as sediments of Siwalik and Indo-Gangetic Plain, (ii) highly resistive (> 1000Ωm) zone below the sediments at a depth of 6 km, interpreted as the top surface of the Indian plate, (iii) a low resistivity (< 10Ωm) below the depth of 6 km near MCT zone coincides with the intense micro-seismic activity in the region. The zone is interpreted as the partial melting or fluid phase at mid crustal depth. Sensitivity test indicates that the major features of the geoelectrical model are relevant and desired by the MT data.     

边坡离心模型试验中的降雨模拟研究

为了在离心机试验中模拟降雨引起的滑坡,设计和使用了一套降雨模拟系统。这套系统的构成主要是针对离心试验的特殊要求进行设计的。所采用的特殊技术可以均匀分配雨水,将雨滴的尺寸效益和科氏加速度引起的雨滴偏移最小化,实现了不同强度和历时的降雨模拟。通过一个降雨条件下砂土边坡的离心模型试验,成功应用了该套降雨模拟系统,研究了边坡中的降雨入渗过程。     

贵州纳雍普洒滑坡动力触发机制离散元模拟分析

采用UDEC离散单元法数值模拟,再现了贵州纳雍张家湾镇普洒滑坡在煤层采空区、深大岩溶裂隙、强降雨和回采爆破振动协同作用下的动力响应特征,揭示出该崩滑的动力触发机制与主控因素。结果表明：（1）在原始坡体下伏煤层自下而上依次开采时,其采空区上覆岩层中“冒落带”、“裂缝带”和“弯曲下沉带”范围逐渐扩大,当位于最上部的煤层被开采后,其上覆岩层中发育的“弯曲下沉带”已触及坡脚;期间该原始坡体处于累积变形阶段,其变形具有明显的整体“下座”和“顺时针旋转”特征;（2）在强降雨作用时,已受采空区作用的坡体进入累积变形扩大阶段,其宏观变形仍具有“下座”和“顺时针旋转”特征;（3）当回采爆破振动持续作用时,已受采空区和强降雨耦合作用的变形坡体进入持续“渐进损伤”、“临界崩滑”、“解体破碎”、“震荡抛射”和“堆积压实”动力响应阶段,期间滑坡体宏观位移表现出明显的“下座”、“溃屈”和“顺时针旋转”特征。     

Finite element modelling of non-linear deformation of rate-dependent materials using a R-minimum strategy

A R-minimum strategy, which was proposed and successfully applied to analyse the non-linear rate-independent finite deformation (including the thermal–mechanical coupling and frictional contact) of elasto-plastic materials, is extended and applied here to simulate the deformation of rate-dependent materials. It involves no iterations, thus belongs to the static-explicit algorithm and avoids the convergence problem resulting from nonlinearities. The R-minimum strategy-based adaptive control scheme of the time step size is proposed and applied to the related analysis of the rate-dependent materials with both the time-dependent and the time-independent viscosity. Both the simple benchmark test and the practical application in evaluation of the effect of the Earth materials on its response to the centrifugal force are carried out to demonstrate the stability, efficiency and usefulness of this algorithm.