顺层岩质边坡渐进破坏及失稳机理的数值模拟研究

提出了利用Lagrangian乘子网格来模拟顺层边坡层间结构面接触行为的方法,并推导了考虑接触约束的Lagrangian控制方程的弱形式及其有限元离散方程。Lagrangian乘子网格容许界面出现较大的切向滑移,较好地解决了接触问题中的高度非线性和响应不平滑性。应用以上方法对沪－蓉－西高速公路某顺层岩质高边坡进行了数值模拟分析,得到了临滑状态下的位移场、应力应变场、结构面上的接触状态、层间滑移距离以及接触摩擦力的分布规律。数值模拟结果表明,顺层岩质边坡的破坏是一个渐进的过程,由最初的层间错动,发展为顺层蠕滑,最后在坡底剪出而破坏;其破坏型式由最初的顺层滑动逐步向溃曲破坏转化。     

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.     

A material model for inelastic rock deformation with spatial variation of pore pressure

This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic-plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.     

Finite element analysis of effect of lining on damage in viscoplastic rocks

This paper presents the constitutive aspects and a finite element application for an energetic damage criterion within Cristescu’s viscoplastic constitutive law. The numerical model is implemented in finite element code LCPC-CESAR [1] by the author. The numerical solution is used to perform an analysis of the evolution of the damage zones around a circular lined cavity in a viscoplastic material subjected to a far field stress. Two important factors regarding the opening stability, namely the lining mounting time and the tunnel face influence, are analyzed. The initial stress of rock mass varies with the depth at which the tunnel is excavated and this fact determines a bigger displacement of the tunnel bottom than the tunnel ceiling. The time emphasizes this asymmetry. The results obtained are in completely accordance with the practical observations.     

A large strain finite element formulation for one dimensional membrane elements

A finite element formulation suitable for large strain analysis of one-dimensional membranes is described which has applications to the analysis of problems in soil mechanics involving reinforced earth. The finite element equations, which are derived for a plane strain iso-parametric element of arbitrary order, are cast in the familiar small displacement form, but with a modified material stiffness matrix. In this formulation, full account is taken of element rotations during each load step, an effect which is important when stresses cease to be insignificant when compared with the material modulus. The method is illustrated with reference to a large displacement test problem which has a known closed form solution. An example is included demonstrating the application of the formulation to the analysis of a reinforced unpaved road.     

A contact problem for a poroelastic halfspace containing an embedded inextensible membrane

The paper examines the axisymmetric problem of the indentation of a poroelastic halfspace that is reinforced with an inextensible permeable/impermeable membrane located at a finite depth by a rigid indenter. The constitutive behavior of the poroelastic halfspace is described by the three-dimensional theory of poroelasticity proposed by M.A. Biot. The contact conditions between the indenter and the poroelastic halfspace are varied to accommodate both adhesive/frictionless contact and impermeable/permeable conditions. The formulation of the mixed boundary value problems uses the stress function approaches applicable to semi-infinite domains. Successive applications of Laplace and Hankel integral transforms are used to reduce the mixed boundary value problems to sets of coupled Fredholm integral equations of the second kind. These integral equations are solved using numerical approaches, applicable both for the solution of the systems of coupled equations and for Laplace transform inversion, to examine the time-dependent displacement of the rigid indenter. The analytical-numerical estimates for the time-dependent displacements of the rigid indenter are compared with results obtained using a finite element approach.     

阶梯式钻头挤土机理的有限元分析

为了分析阶梯钻头冲击挤密作用下土体的变形机理,将土体视为DP材料,服从Drucker-Prager屈服准则,通过钻具与土体之间的接触以及施加冲击载荷来模拟钻进过程,建立了潜孔锤冲击挤密钻进的有限元模型。以非线性瞬态动力学有限元分析为手段,利用有限元软件ANSYS9.0对阶梯钻头冲击挤密作用下土体的变形机理进行了模拟分析。结果表明,在冲击载荷作用下,冲击功主要用于竖向压缩土体,水平方向的挤压作用相对较小。阶梯钻头对土体的破坏作用可以看作是每个台阶的微剪切作用,当台阶布置合理时,土体沿等效锥面整体破坏,破坏后的土体在等效锥面的作用下被挤向孔壁四周,挤密效果较好。      

顺层路堑边坡锚杆支护稳定性的有限元模拟分析

基于理想弹塑性本构模型和Drucker-Prager准则,运用ANSYS软件和有限元数值模拟技术,建立了顺层岩体边坡的有限元分析模型。结合沪蓉国道主干线宜昌至恩施公路白氏坪-榔坪段顺层路堑高边坡工程实例,对顺层岩体路堑边坡布设锚杆支护前后的应力、变形和稳定性进行了模拟分析。分析比较表明,锚杆支护结构可以减小边坡临界状态下的最大位移、增大最危险接触面的摩擦力和提高边坡的稳定性系数,从而能有效地提高边坡的稳定性以防止顺层滑坡的发生。     

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.     

格型钢板桩结构有限元数值分析

以有限元软件ABAQUS作为分析平台,建立波浪荷载作用下格型钢板桩结构稳定性及应力分析的三维弹塑性有限元分析模型。格型钢板桩采用壳体单元模拟,在相邻板桩之间设置铰接连接器模拟板桩之间的相对转动;土体采用Mohr-Coulomb本构模型模拟,在格型钢板桩与其内、外土体之间设置接触面单元模拟它们之间的滑移、张裂和闭合。结合某实际工程,研究结构的破坏模式、失稳特性和应力分布特性,分析参数变化对结构稳定性和环向拉力的影响,并对格内土体的剪切变形进行分析,建议格型钢板桩锁口拉力的验算断面。结果表明,铰接连接器的设置对于结构稳定性影响不大,但对环向拉力有一定影响;格内土体的剪切变形主要发生在格体中轴处,符合太沙基法结论。     

A NON-LINEAR SEISMIC RESPONSE ANALYSIS METHOD FOR SATURATED SOIL–STRUCTURE SYSTEM WITH ABSORBING BOUNDARY

A non-linear seismic response analysis method for 2-D saturated soil–structure system with an absorbing boundary is presented. According to the 3-D strain space multimechanism model for the cyclic mobility of sandy soil, a constitutive expression for the plane strain condition is first given. Next, based on Biot's two-phase mixture theory, the finite element equations of motion for a saturated soil–structure system with an absorbing boundary during earthquake loadings are derived. A simulation of the shaking table test is performed by applying the proposed constitutive model. The effectiveness of the absorbing boundary is examined for the 2-D non-linear finite element models subjected to random inputs. Finally, a numerical seismic response analysis for a typical saturated soil–structure system is performed as an application of the proposed method.     

砂土液化变形的有限元-无网格耦合方法

通过构造Biot固结理论u-p方程的无网格伽辽金-有限元耦合方法,对砂土液化变形问题进行了数值模拟。对于饱和砂土,采用Oka等提出的弹塑性本构模型,同时采用更新的Lagrange计算格式推导了控制方程。耦合方法能够发挥有限元和无网格各自的优点,既避免了由于单元变形扭曲而引起的计算中断,也可节约计算时间,算例验证了该方法在地震液化问题中的有效性。     

考虑桩-土非线性接触的自平衡桩基测试有限元分析

自平衡桩基测试由于不受场地限制,在桥梁桩基检测和水上试桩领域得到较为广泛应用,但由于自身承受荷载机理、桩土相互作用与传统桩基静载测试不同,目前其实际应用仍然存在一些问题,因此需要在自平衡加载方式下建立合理数值模型来为进一步理论分析奠定模型基础。在考虑桩体非线性接触面基础上,研究了决定非线性接触性质的摩擦系数计算原则及相关模型参数取值,基于ANSYS接触面单元建立了自平衡桩基有限元模型,以武汉工程为依托,与实测结果进行对比,结果表明基于接触面单元建立的自平衡桩基模型具有更高的精确度,能够很好反映真实荷载作用下上下段桩位移曲线图。     

Instability of gradient dependent elasto-viscoplasticity for clay

A gradient-dependent viscoplastic constitutive model for water saturated clay is proposed to describe the strain localization phenomena and pattern formation during deformation. Second- and fourth-order gradients of volumetric viscoplastic strain are introduced into the constitutive equations to account for the non-local effects due to the motion of microstructures. A linear perturbation analysis is applied to this model. The instability of the government equations (i.e. the constitutive equations and the equations of motion for the clay skeleton and pore water) is discussed for both the one-dimensional and the two-dimensional situations. In addition, issues concerned with the formulation of boundary value problems by finite element analysis in relation to the formulation and the boundary conditions are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Multi-laminate framework of soil models—plasticity formulation

This paper presents plasticity formulation of the multi-laminate framework of soil models. Soil element is assumed to be an assemblage of perfectly fitting polyhedral blocks and irreversible deformations are assumed to occur due to sliding, separation/closing of the boundaries. Using an appropriate summation of mechanisms, the total plastic strains are obtained by evaluating contributions from an infinite number of randomly oriented planes in space. The paper provides a general plasticity formulation and examines various constitutive theories which can be incorporated into the framework.     

A fully coupled thermo-hydro-mechanical nonlinear model for a frozen medium

This paper describes a nonlinear elasto-plastic simulation of freezing and thawing of rock. A mathematical formulation is described in which deformation, fluid flow and heat flow are fully coupled. A non-linear elasto-plastic constitutive relationship is presented and a two dimensional (plane stress) numerical modeling is performed based on the finite element method applied to thermo-poro-elastoplasticity. It is assumed that the Mohr-Coulomb's failure criterion is valid for yield locus and plastic potential. The numerical scheme employed in the code accommodates phase change of pore-water from liquid to solid (ice). The primary aim of this paper is to compare the temperature transfer and deformation prediction obtained from the numerical code with those obtained from the freezing and thawing experiments. It is found from the numerical simulation that a relatively good prediction can be made of temperature transfer and deformation behavior. The numerical code has also been applied to a hypothetical cavern problem to demonstrate its applicability.     

弹塑性无厚度接触面单元的本构积分算法及验证

对基于理想弹塑性理论框架、屈服准则为Mohr-Coulomb准则、采用非关联流动法则的无厚度接触面单元的本构积分算法进行了探讨,引入非关联的伪屈服函数和伪势函数,提出了将超出屈服面、处于角点应力区的试应力双向返回到屈服面的本构积分算法。据此编制了ABAQUS用户单元子程序,进行了算例验证。结果表明,提出的算法可以较好地实现土与结构物共同作用的有限元数值模拟。     

Finite element formulation and algorithms for unsaturated soils. Part I: Theory

This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd.