Discrete numerical modelling of rockfill dams

The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC^2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Discrete element modelling of creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the discrete element model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013). The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution.     

堆石蠕变机理分析与颗粒破碎特性研究

根据大型压缩仪完成的堆石蠕变试验,结合颗粒破碎测试试验,对蠕变产生的机理进行了简要的理论分析,在力的作用下,细化破碎的堆石颗粒滑移充填孔隙是发生蠕变的重要原因。堆石颗粒的破碎可分为对应于主压缩变形的颗粒破碎和伴随蠕变变形的颗粒破碎。颗粒破碎引起堆石级配的细微改变,从而形成后期变形。     

Modelling the time‐dependent behaviour of granular material with hypoplasticity

This paper presents a constitutive model for time‐dependent behaviour of granular material. The model consists of 2 parts representing the inviscid and viscous behaviour of granular materials. The inviscid part is a rate‐independent hypoplastic constitutive model. The viscous part is represented by a rheological model, which contains a high‐order term denoting the strain acceleration. The proposed model is validated by simulating some element tests on granular soils. Our model is able to model not only the non‐isotach behaviour but also the 3 creep stages, namely, primary, secondary, and tertiary creep, in a unified way.     

Fuzzy parameters analysis of time‐dependent fracture of concrete dam models

In order to apply the mechanical properties (measured on material specimens or laboratory‐sized models) to large structures (such as concrete dams), a non‐linear theory able to predict the size‐scale effect has to be used. One of these theories was first proposed by Hillerborg and co‐workers (fictitious crack model) and is based on the earlier works by Barenblatt and Dugdale for metals (cohesive crack model). It is based on the existence of a fracture process zone (FPZ), where the material undergoes strain softening. The behaviour of the material outside the FPZ is linear elastic. A large number of short‐time laboratory tests were executed, by varying the load, under crack mouth opening displacement control. Since concrete exhibits a time‐dependent behaviour, an interaction between creep and micro‐crack growth occurs in the FPZ. Therefore, different testing conditions can be applied: rupture can be achieved by keeping the load constant before peak value (pre‐peak tests), or after peak value and after an unloading and reloading procedure (post‐peak tests). The crack propagation rate is shown to be small enough to neglect inertial forces and large enough to keep the time‐dependent behaviour of the process zone as dominant compared to the behaviour of the undamaged and viscoelastic zone. Due to the variability in material microstructure from one specimen to another, experimental data show large ranges of scatter. Well established methods in probability theory require sufficient experimental data in order to assume a probability density distribution. The objective of this study is to investigate the ranges of variation of the time response under constant load in simple structural elements associated with pre‐selected variation (fuzziness) in the main material parameters. For situations where the values of the material parameters are of a non‐stochastic nature, the fuzzy set approach to modelling variability has been proposed as a better and more natural approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Settlement‐time behaviour of granular embankments

Creep settlements are the main cause of deterioration of road pavement and impervious elements of dams, and therefore a method to calculate them is needed. Viscoelastic models (e.g. the standard linear solid) have been chosen to represent the creep of granular materials (Figure 1). Finite element calculations show that quasi‐oedometric conditions exist near the centre of embankments. Explicit expressions for one‐dimensional viscoelastic settlements of an embankment during and after construction have been obtained for any loading law and drawn for a linear load. The three viscoelastic parameters, E_o, R_c and T_r can be determined through laboratory or field testing, and the results can be adjusted by using settlement records. Good agreement has been found between measured and calculated settlements at several dams. Copyright © 2000 John Wiley & Sons, Ltd.     

Delayed plastic model for time‐dependent behaviour of materials

A delayed plastic model, based on the theory of plasticity, is proposed to represent the time‐dependent behaviour of materials. It is assumed in this model that the stress can lie outside the yield surface and the conjugate stress called static stress is defined on the yield surface. The stress–strain relation is calculated based on the plastic theory embedding the static stress. Thus, the stress–strain relation of the model practically corresponds to that of the inviscid elastoplastic model under fairly low rate deformation. The delayed plastic model is coupled with the Cam‐clay model for normally consolidated clays. The performance of the model is then examined by comparing the model predictions with reported time‐dependent behaviour of clays under undrained triaxial conditions. It is shown that the model is capable of predicting the effect of strain rate during undrained shear and the undrained creep behaviour including creep rupture. Copyright © 2001 John Wiley & Sons, Ltd.     

高混凝土面板堆石坝流变的三维有限元数值模拟

采用一种新的能模拟高围压条件的堆石料幂函数流变本构模型,对水布垭面板堆石坝进行了考虑堆石料流变特性的应力-应变仿真分析。结果表明,考虑堆石料流变特性后的坝体变形有明显的增加,坝体应力有所松弛。堆石体的流变特性使得面板的挠度有所增加,面板顺坡向和坝轴向拉应力极值有所增大。对于分期浇筑面板、分期蓄水的高混凝土面板堆石坝,选用合适的流变本构模型正确地模拟堆石体的流变特性,其结果可以为大坝填筑进度及面板分期浇筑时间的确定提供参考,对于正确地预测大坝的应力变形也具有重要意义。     

考虑拱效应的高面板堆石坝流变收敛机制研究

采用一种能模拟高围压条件的堆石料幂函数流变本构模型,探讨狭窄河谷条件下堆石体流变变形的发展规律及相应的控制流变变形的工程措施。数值仿真结果表明,在狭窄河谷中的堆石体存在着拱效应。由于拱效应的影响,如果不考虑堆石体流变导致拱效应减弱而增加的附加变形,数值仿真计算得到的大坝变形将小于其真实的变形。受拱效应影响,堆石体初期变形的速率受到抑制,但随着坝体的升高、蓄水后水压力的加大以及堆石体随时间发展等流变变形因素的影响,堆石体中的拱效应逐渐减弱。要减小面板浇筑后由于其下卧的堆石体流变产生的附加变形,可以尽量利用面板过水及堆石体挡水,以加快堆石体流变变形的完成。采取措施,避免大的陡坡突变以及面板浇筑时间滞后其下卧堆石体断面几个月。     

Discrete element modelling of material non‐coaxiality in simple shear flows

We investigate the quasi‐static simple shear flow of a two‐dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised‐wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non‐coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non‐coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction. © 2013 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons, Ltd.     

考虑堆石体流变效应的高面板坝最优施工程序研究

考虑高面板坝堆石体的流变变形效应对堆石体的最优施工碾压进度方案进行了研究。结果表明,堆石体的本身流变变形特性对不同施工碾压进度方案下的面板垫层变形影响较大。堆石坝不同材料分区的特点从客观上决定了高堆石坝必然存在一个较优的施工填筑上升方案。堆石体均匀上升的填筑进度方案的面板垫层法向最大位移较小,且沿面板坡向的分布比较均匀,对面板与垫层间的协调变形有利。从最优填筑方案的角度来看,建议高堆石坝采用均匀上升的碾压施工程序。     

Elasto‐plastic modelling of stress‐path‐dependent behaviour of interfaces

A single‐surface elasto‐plastic model developed by Desai and his coworkers is used to predict the behaviour of an interface between sand and a steel plate. The loading in the experiments and in their predictions followed various stress and displacement paths. The results of predictions of the two‐ and three‐dimensional behaviour of the interface under both constant normal stress and constant normal stiffness conditions are presented. The predictions are compared with their corresponding experimental results. The model parameters were determined on the basis of 2‐D conventional experiments under the condition of constant normal stress and they were used in the prediction of the interface behaviour in various stress paths. There is, in general, a good agreement between the predicted and experimental results. Copyright © 2000 John Wiley & Sons, Ltd.     

混凝土面板堆石坝蠕变沉降经验模型及其应用

根据岩土材料Merchant、Bergers和Butterfield蠕变模型的基本形式,建立3种预测混凝土面板堆石坝蠕变沉降经验模型。以蒲石河混凝土面板堆石坝为例,采用非线性有限元方法数值模拟堆石坝的顺序填筑过程。根据堆石坝沉降现场观测数据,采用回归分析方法确定3种沉降经验模型中的待定参数,确定堆石坝的蠕变沉降随时间的变化关系。工程实践应用结果表明,所提出的堆石坝蠕变沉降经验模型具有较高的拟合和预测精度,堆石坝的蠕变沉降除与时间有关之外,还与观测点的应力状态和位置以及堆石料的变形模量有关。     

深厚覆盖层上高砾石土心墙堆石坝变形监测分析

在深厚覆盖层上建筑的高砾石土心墙堆石坝得到迅猛发展的同时,正确地认识坝体变形规律和合理地数值模拟是不可忽视的问题。堆石坝变形的影响因素多且复杂,监测成果的分析对研究上述问题具有重要意义。以硗碛大坝的监测资料为基础,结合坝体的填筑和蓄水过程,对位于深厚覆盖层上的百米级砾石土心墙堆石坝的变形规律进行了系统分析,并与其坝高、覆盖层深度、河谷宽度等方面都具有相似性的毛尔盖大坝监测资料进行了对比分析。通过分析两座大坝监测结果,对坝体的变形特性进行了规律性总结,对湿化和蠕变作用以及水库填筑和蓄水过程对坝体变形的影响有了一定认识。分析结论可为正确认识以及合理模拟和预测同类坝体的变形特性提供参考和依据。     

Discrete element modelling of fragmentable geomaterials with size dependent strength

This paper presents the application of a discrete element technique to the analysis of the dynamic indentation of either a purely brittle or a brittle viscoplastic geomaterial which can experience fragmentation resulting in fragments with size dependent strength characteristics.     

Three‐dimensional numerical analysis of concrete‐faced rockfill dam using dual‐mortar finite element method with mixed tangential contact constraints

Concrete‐faced rockfill dam (CFRD) is a popular alternative to traditional dam types in the last two decades. The modelling of CFRD involves complex multi‐body contact and strong geometry and material nonlinearities. We present a numerical approach for the modelling of CFRDs in this paper. Based on the dual‐mortar finite element method, the presented approach considers different parts of rockfill and all concrete slabs as independent deformable continuum. The multi‐body contacts are modelled using Lagrange multipliers with a weak form segment‐to‐segment contact strategy. To alleviate instability induced by strong geometry nonlinearity in the slab–slab contact, we propose a mixed type of constraints for the tangential contact. A general transformation scheme is introduced to simplify the implementation of contact constraints. Three‐dimensional analysis of Tianshengqiao‐1 CFRD is performed. The nonlinear and time‐dependent deformation of the rockfill is considered. We study the influence of the rockfill deformation on the reliability of the concrete face. Three major concerns of the face, that is, the axial compression, the slab–slab separation and the face‐rockfill separation, are discussed in detail. The numerical results are compared with data from in‐situ observation. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical evaluation of soft inter‐slab joint in concrete‐faced rockfill dam with dual mortar finite element method

Recently constructed concrete‐faced rockfill dams (CFRDs) often use soft inter‐slab joints to prevent axial compression‐induced extrusion damage in the concrete face. Due to the complexity of the multibody contact and the lack of information on the actual behavior of soft joints, it is highly challenging to numerically assess the effect of soft joints in CFRDs. In this paper, we present a numerical approach for the three‐dimensional modeling of CFRDs with hard and soft joints. A dual mortar finite element method with Lagrange multiplier is developed to treat the multibody contact in hard joints with impenetrability condition. The soft joint slab‐filler‐slab contact system is modeled using an equivalent contact interface approach, where the soft contact constraints are imposed using a perturbed Lagrange formulation. Through a series of laboratory tests, the mechanical behavior of soft joint is investigated. An extrusion model for the soft joint is presented and implemented in the dual mortar finite element method. The proposed numerical method is applied to the three‐dimensional analysis of Tianshengqiao‐1 CFRD. Despite the complex multibody contact and strong material and geometry nonlinearities in the CFRD, the proposed method is stable and capable of capturing salient characteristics of the CFRD. Numerical results show that in Tianshengqiao‐1, the employment of soft joints can effectively reduce the axial compression stress, thus greatly alleviating the risk of extrusion damage in the concrete face.     

Discrete element modelling of an underground explosion in a jointed rock mass

The purpose of this paper is to investigate the application of the discrete element program UDEC for modelling underground explosions in a jointed rock mass. A field underground explosion test has been conducted and UDEC and AUTODYN were utilised in a coupled manner to predict the rock mass response due to the underground explosion. The dynamic equation for the state of the rock material obtained from impact tests was incorporated into the calibration modelling. The comparison of modelling results with test results and empirical formulas shows that UDEC is capable of modelling explosion wave propagation in jointed rock mass with high reliability.     

Study on wetting deformation characteristics of coarse granular materials and its simulation in core-wall rockfill dams

The wetting deformation of coarse granular materials is often considered to be an important cause of the core wall rockfill dam cracks during impounding. By analyzing existing research results, this paper proposes a hyperbolic relationship between the wetting axial strain and wetting stress level and puts forwards a warped surface relationship among spherical stress, shear stress, and the ratio of wetting volumetric strain to wetting axial strain. To illustrate its practicability, the wetting strain model's parameter determination process is introduced and the rockfill materials wetting parameters are determined using the triaxial wetting test data. Moreover, the collapse settlement of Guanyinyan rockfill dam during first impounding is numerically simulated using the proposed method to calculate rockfill wetting deformation and verified by field measurements and monitoring data. The results show that the calculative method of wetting deformation proposed in this paper is reasonable and practical; the wetting deformation of upstream rockfill materials would cause an adverse deformation trend, which may lead to crack occurrence at the upstream slope and dam crest; and the Guanyinyan rockfill dam cracks on the top of junction mainly caused by the wetting deformation of upstream rockfill.