A parameter identification procedure for viscoelastic materials

A parameter identification procedure is presented for visco-elastic materials. The idea of this method is based on the boundary control concept by using the dual properties of traction and displacement, for example, if we give the traction force on a traction boundary and we observe displacement on a part of the same boundary (the observational or control boundary condition), then we may determine the material properties corresponding to the given and observed data. The numerical procedure is then developed on the basis of Newton’s iteration scheme. The method has been shown to be effective for a linear elastic material Ichikawa and Ohkami, Soils and Foundations, 1992, 32(2), 35–44 and for damage mechanics problems Tsuchiyama et al., Journal of Geotechnical Engineering, Japan Society of Civil Engineers, 1993, 475/III -24, 49–58 (in Japanese). In this paper we give an extension to the visco-elastic problem.     

A method of time-dependent analysis using elastic solutions for nonlinear materials

The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.     

A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

颗粒离散单元法动力人工边界设置方法

采用颗粒离散单元法进行动力计算时,人工截断边界上需设置吸收边界条件,以防止波的反射。鉴于颗粒离散单元数值计算模型的人工边界上颗粒单元半径大小不一、边界面凸凹不平,在连续介质的黏性、黏弹性、自由场边界条件方程基础之上,推导出适用于离散介质的等效方程。在离散介质的黏性边界条件等效方程中引入微调系数,提出比值迭代法以快速确定其最优值,以实现对波的最佳吸收。采用二维颗粒离散单元计算软件PFC2D,分别建立黏性、黏弹性、自由场边界条件相关数值分析模型,探讨颗粒分布模式对黏性边界上颗粒单元半径、速度分布及比值迭代过程的影响;采用外源波动算例及经典Lamb问题算例验证黏弹性边界设置方法的正确性;通过隧洞算例检验提出的自由场边界条件设置方法的正确性。     

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

Simulation of frictional contact between soils and rigid or deformable structure in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two algorithms are implemented into the SPH code to describe contact behavior, where the contact forces are calculated using the law of conservation of momentum based on ideal plastic collision or using the criteria of partial penetrating. In both algorithms, the problem of boundary deficiency inherited from SPH is properly handled so that the particles located at contact boundary can have precise acceleration, which is critical for contact detection. And the movement and rotation of the rigid structure are taken into account so that it is easy to simulate the process of pile driving or movement of a retaining wall in geotechnical engineering analysis. Furthermore, the capability of modeling deformability of a structure during frictional contact simulations broadens the fields of SPH application. In contrast to previous work dealing with contact in SPH, which usually use particle‐to‐particle contact or ignoring sliding between particles and solid structure, the method proposed here is more efficient and accurate, and it is suitable to simulate interaction between soft materials and rigid or deformable structures, which are very common in geotechnical engineering. A number of numerical tests are carried out to verify the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions or results from finite element method analysis. Good agreement obtained from these comparisons suggests that the proposed algorithms are robust and can be applied to extend the capability of SPH in solving geotechnical problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Visco‐elastic load transfer models for axially loaded piles

Viscoelastic or creep behaviour can have a significant influence on the load transfer (t–z) response at the pile–soil interface, and thus on the pile load settlement relationship. Many experimental and theoretical models for pile load transfer behaviour have been presented. However, none of these has led to a closed‐form expression which captures both non‐linearity and viscoelastic behaviour of the soil. In this paper, non‐linear viscoelastic shaft and base load transfer (t–z) models are presented, based on integration of a generalized viscoelastic stress–strain model for the soil. The resulting shaft model is verified through published field and laboratory test data. With these models, the previous closed‐form solutions evolved for a pile in a non‐homogeneous media have been readily extended to account for visco‐elastic response. For 1‐step loading case, the closed‐form predictions have been verified extensively with previous more rigorous numerical analysis, and with the new GASPILE program analysis. Parametric studies on two kinds of commonly encountered loading: step loading, ramp (linear increase followed by sustained) loading have been performed. Two examples of the prediction of the effects of creep on the load settlement relationship by the solutions and the program GASPILE, have been presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Some aspects of coupled FEBEM analysis of underground openings

The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM.     

用孔压静力触探和室内固结试验求取土的固结系数的对比研究

土的固结系数是软土地基计算与处理设计中的关键参数，本文根据先进的孔隙水压力静力触探技术现场测试求出的固结系数和室内固结试验所求固结系数，进行了大量统计对比研究，发现两者之间存在很好的线性相关关系，并论述了两种方法求取固结系数的原理及步骤，以及孔压静力触探求固结系数的许多优点。     

自然单元法在岩土工程中应用两例

自然单元法(NEM)是较近出现的一种无网格方法,其形函数兼有无网格的特点和传统有限元的优点,是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性,并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟,研究表明,在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同;而在一般的无网格方法中,则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟,引入了无界单元;由于自然单元法的特性,自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。     

新型边界积分方程的无单元解及其应用

目前隧道及大型地下工程往往在裂隙岩体中开挖,而裂隙与地下空间的距离及裂隙的扩展条件,制约着隧道及地下工程的稳定性。应用能考虑孔洞和裂纹问题的新型边界积分方程与无网格加辽金法结合,建立一种新型的边界无单元法。在该方法中基本的未知量是由边界上的面力和边界上位移密度函数构成的复变量边界函数 。文中应用的边界积分公式和Muskhelishvili的积分公式直接相关。将无网格构造方法引入新型的边界积分方程,建立了新型的边界无单元法。应用该方法详细分析了含隧道和裂纹间相互关系等问题,其数值结果与解析结果吻合很好,说明该方法的正确性和可行性。     

软土地基沉降的二维非线性粘弹性反演与预测

基于Merchant粘弹性模型和简化双曲线模型，建立软土地基沉降的二维非线性粘弹性Biot固结有限元计算公式；根据最小二乘法建立目标函数，采用Simplex直接优化算法反演确定参数；为反演能获得在物理意义上合理且数学上唯一的参数，提出从简单模型到复杂模型的分步反演分析方法。实例分析表明，该方法是可行的。     

采用Laplace变换分析桩基应力波传播问题

将土体中的混凝土桩基简化为黏滞介质中的一维黏弹性杆,桩顶部受锤头冲击产生内部应力波。根据杆内微元应力平衡条件建立杆中一维黏弹性应力波传播的控制方程,结合桩顶锤头冲击条件和桩底弹-黏性约束条件给出桩基两端的耦合边界条件。对控制方程和定解条件作Laplace变换并求解变换后的常微分方程,得到变换域的应力像函数解析解。采用数值反变换技术将像函数转变为时间域的应力波形。应用此方法可以较方便地分析桩基中应力波的产生、传播、反射及相互作用过程。     

地基非线性波动问题中黏-弹性人工边界研究

建立了考虑地基动力非线性效应的波动模拟的二维和三维黏-弹性人工边界条件。引入考虑动力非线性特征的土体等效线性模型中的动模量变化模式,推导了新的平面内法向、平面内切向以及出平面切向的黏-弹性人工边界公式,同时也给出了新的三维法向、切向黏-弹性人工边界公式,并在实际应用中采用等效线性化方法处理,进行了数值算例分析,结果表明,新的黏-弹性人工边界具有更好的精度,可以用于地基非线性波动问题的研究。     

A constitutive model for the dynamic and high‐pressure behaviour of a propellant‐like material: Part I: Experimental background and general structure of the model

This paper is the first part of a work that aims at developing a mechanical model for the behaviour of propellant‐like materials under high confining pressure and strain rate. The behaviour of a typical material is investigated experimentally. Several microstructural deformation processes are identified and correlated with loading conditions. The resulting behaviour is complex, non‐linear, and characterized by multiple couplings. The general structure of a relevant model is sought using a thermodynamic framework. A viscoelastic‐viscoplastic‐compaction model structure is derived under suitable simplifying assumptions, in the framework of finite, though moderate, strains. Model development, identification and numerical applications are given in the companion paper. Copyright © 2001 John Wiley & Sons, Ltd.     

Viscoelastic analysis of piles and pile groups

The axial and lateral load–displacement response of single piles and pile groups during the secondary consolidation (creep) phase of deformation is obtained by idealizing the soil as a linear viscoelastic material. The boundary element method is used to model the soil halfspace and the piles, which are assumed to behave elastically, are idealized as beam-columns. By using the correspondence principle, the problem is solved in the Laplace transform domain and the final solution is obtained by numerical inversion of the transformed data. The salient features of the viscoelastic response are identified in several non-dimensional plots which encompass the spectrum of geometrical and material parameters commonly encountered in practice. The results of the analysis compare favourably with the limited data available in the literature.     

Rheological and physical characteristics of crustal-scaled materials for centrifuge analogue modelling

We characterize a set of analogue materials used for centrifuge analogue modelling simulating deformation at different levels in the crust simultaneously. Specifically, we improve the rheological characterization in the linear viscoelastic region of materials for the lower and middle crust, and cohesive synthetic sands without petroleum-binding agents for the upper crust. Viscoelastic materials used in centrifuge analogue modelling demonstrate complex dynamic behaviour, so viscosity alone is insufficient to determine if a material will be an effective analogue. Two series of experiments were conducted using an oscillating bi-conical plate rheometer to measure the storage and loss moduli and complex viscosities of several modelling clays and silicone putties. Tested materials exhibited viscoelastic and shear-thinning behaviour. The silicone putties and some modelling clays demonstrated viscous-dominant behaviour and reached Newtonian plateaus at strain rates < 0.5 × 10⁻² s⁻¹, while other modelling clays demonstrated elastic-dominant power-law relationships. Based on these results, the elastic-dominant modelling clay is recommended as an analogue for basement cratons. Inherently cohesive synthetic sands produce fine-detailed fault and fracture patterns, and developed thrust, strike-slip, and extensional faults in simple centrifuge test models. These synthetic sands are recommended as analogues for the brittle upper crust. These new results increase the accuracy of scaling analogue models to prototype. Additionally, with the characterization of three new materials, we propose a complete lithospheric profile of analogue materials for centrifuge modelling, allowing future studies to replicate a broader range of crustal deformation behaviours.     

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.     

Calculation of the volume of an alluvial fan

Calculation of the volume of a lithostratigraphic unit within an alluvial fan allows a longterm denudation rate to be calculated for the fan's catchment, where sediment is not transported beyond the fan. The calculation of denudation rates in this case depends upon accurate estimates of the volume of sediment in a lithostratigraphic unit of known age. Two methods of volume calculation and their approximations are presented. The first method sums the volume of discrete blocks used to approximate a variety of fan shapes. The second method integrates a quadratic function that approximates both the surface and lower boundary of a lithostratigraphic unit where the edges of the fan are assumed to be vertical. For fans that satisfy these restrictive assumptions, the integration method should be more accurate than the summation method. However, the summation method is more generally applicable and calculations using the two methods, and their approximations, yield remarkably similar results.