冻土水热耦合方程及数值模拟研究

路基冻胀融沉是多年冻土区路基的主要病害。冻胀融沉病害与土体水分迁移以及温度变化密切相关,而冻土温度变化和水分迁移又会相互影响。基于非饱和土渗流和热传导理论,建立冻土水热耦合问题的联合求解微分方程;然后采用COMSOL Multi-physics软件进行二次开发,实现冻土温度场和水分场全耦合数值模拟;进而将数值模拟结果与土柱冻结和融化实验的结果进行对比,验证水热耦合数值模拟模型的有效性;最后以青海省玛多县地区路基为例,研究多年冻土路基中温度场与水分场的分布和变化规律。     

颗粒材料的离散颗粒及间隙水渗流模型与数值模拟

基于离散颗粒模型的含间隙水颗粒材料液-固耦合分析，发展了Darcy渗流模型。应用特征线SPH方法求解液相，建立饱和与非饱和颗粒材料渗流模型的数值模型。数值例题给出饱和颗粒材料结构物在位移加载条件下的破坏模式及间隙水Darcy速度与水压力分布，并进一步模拟降雨条件下非饱和颗粒材料结构物的瞬态渗流过程，显示该模型模拟含间隙水颗粒材料结构物液-固耦合及变形的良好性能。     

水土耦合SPH数值模型的正则化修正及其应用

传统光滑粒子流体动力学(smoothed particle hydrodynamics,简称SPH)方法的光滑粒子近似在粒子数量不足的区域可能导致场函数及其梯度的不合理评价,从而引起物理量的非正常波动,即张力不稳定问题(tensile instability)。针对当前研究较少关注岩土工程SPH方法精度问题的现状,提出了一种基于正则化修正的水土耦合SPH数值模型,较好地避免了张力不稳定问题。在提出的模型中,根据Biot固结原理将固相(土骨架)和液相(孔隙水)分配到不同的计算层,同时通过状态方程计算液相的压力变化,采用弹性模型描述土骨架的应力–应变关系。在三维水体溃坝模型的模拟、无地下水和有地下水的堤防自重应力分析中应用了提出的SPH模型,并对比分析了有限元、未修正SPH和修正SPH计算结果,表明基于正则化修正的SPH模型较未修正模型具有更好的精度,为SPH方法在岩土体渐进式破坏问题上的应用提供了重要的参考意义。     

非饱和土中热湿盐多场耦合过程分析

以多孔介质理论为基础研究了非稳态条件下非饱和土中温度–水分–盐分多场耦合问题。考虑到非饱和土中孔隙被液态水、溶解的盐分、水蒸气和干燥气体等填充,在质量和能量守恒的基础上获得了非饱和土中水分、气体、盐分的质量守恒方程以及能量守恒方程。考虑一维非稳态问题,选取温度、孔隙气压、孔隙水压和含盐量以及其梯度作为状态变量,得到问题的状态方程组。利用Laplace变换将时域上的状态方程转换到频域上,在给定的边界条件下,采用打靶法求解该强耦合的非线性变系数微分方程组。基于Hausdorff矩问题的稳定化算法将频域上的数值解转化到时域上,通过与已有的试验结果相比较,验证了模型的有效性。基于数值算例与参数,分析了压力梯度、温度梯度、孔隙率等条件对非饱和中温度场、水分场和盐分场分布的影响规律。     

非饱和岩土介质渗流问题的光滑粒子法模拟

 非饱和土渗流问题在大坝渗流、降雨入渗、垃圾填埋场内部污染物扩散等领域有着广泛的应用。对非饱和渗流Richards方程的数值求解,一直以来多是采用有限单元法计算基质吸力水头为自变量的方程进行的。但是,材料属性的高度非线性特征会导致数值解的质量守恒性质较差及非物理性震荡,同时可能引起迭代过程的不收敛。尝试着将光滑粒子法引入到基质吸力水头形式Richards方程的求解中,以便获得具有质量守恒特性的数值解,并通过数值算例验证其实用性和可靠性,从而为此类问题的求解提供一种新的思路。最后,采用基于光滑粒子法编写的程序模拟了蒸发条件下的一个复杂非饱和渗流问题,这对实际的工程应用有一定的借鉴价值。     

不排水条件下非饱和土水力–力学耦合特性数值模拟

非饱和土即便在不排水、不排气条件下也将发生体变,这为预测非饱和土不排水、不排气力学特性带来了困难。基于三相孔隙介质理论,结合非饱和土的弹塑性本构模型推导了不排水、不排气条件下非饱和土三轴剪切三相耦合控制方程,对非饱和土的不排水、不排气三轴剪切特性进行预测。数值模拟结果表明,此方法能够描述非饱和土在不排水、不排气条件下的水力–力学特性,如体缩特性、孔隙水压力和孔隙气压力增长以及饱和度增大等特性。数值计算结果与室内试验结果一致,证实了所提数值分析方法的合理性。     

变热源强度温度荷载作用下非饱和土中的水分迁移规律研究

给出非饱和土中热能传输和水分迁移的耦合控制微分方程。假定无限介质内热源的存在引起周围多孔介质内温度的瞬态变化和水分的迁移和扩散。利用多重Fourier变换、Laplace变换给出其在变换域上的解,然后利用热源函数法给出瞬时点热源条件下非稳态温度场、体积含水率分布场的解析求解方法。通过在时间域上和空间域上进行积分,建立热源强度随时间变化的球域热源情况下的数值积分求解方法,给出温度场作用下多孔介质内水分迁移的演化规律和分布特征。     

薄钢板在高速碰撞载荷作用下的数值算法

探讨了SPH算法的基本原理及该方法的优缺点;采用该算法对柱形杆高速冲击钢制薄靶板的击穿、粒子飞溅及碎片云的形成过程进行了数值模拟;解决了四棱柱形钢杆SPH粒子单元模型的建立问题,分析了作用过程的物理机理;表明SPH算法可以用于解决高速冲击动力学问题,模拟和预测材料在高速碰撞下的瞬态响应。     

水力–力学耦合的超固结非饱和土本构模型的隐式积分算法及其应用

超固结非饱和土经常出现于工程实践中,表现出复杂的力学性质。从已有的非饱和土水力–力学耦合的本构模型出发,将超固结的影响加入到了模型中,使模型可以考虑超固结对非饱和土力学性质的影响。超固结非饱和土本构方程的求解是一个复杂的非线性问题,给出了该超固结非饱和土水力–力学耦合模型的隐式积分算法和本构模型的一致切线模量,并对该算法进行验证,证明了该算法的正确性,最后采用该算法对某非饱和土质边坡在地下水位上升的情况下进行有限元分析。     

多孔介质中两相流动过程的毛细滞回效应

 含水量大小以及干湿循环变化历史对多孔介质渗流过程有着重要影响。基于多孔介质理论和毛细滞回内变量模型,建立能够考虑含水量变化历史影响的多孔介质两相流动模型,并利用开发的U-DYSAC2有限元程序进行相应的数值模拟。通过模拟结果与试验数据的比较,验证所建数值模型在模拟复杂条件下非饱和多孔介质渗流问题的可靠性与有效性。对干湿循环变化条件下土质边坡渗流过程进行数值分析,结果表明：毛细滞回效应对非饱和土渗流过程具有显著影响,非饱和土水力状态不仅取决于当前含水量或基质吸力大小,而且还与土体所经历的水力历史有关;特别地,如果利用主脱湿线来描述土水特征关系,那么土体中基质吸力的预测结果会偏高,从而使得传统边坡稳定性分析方法高估土体抗剪强度以及坡体安全系数。因此,在模拟非饱和多孔介质复杂渗流问题时必须要考虑毛细滞回效应。     

Soil–water–air fully coupling finite element analysis of slope failure in unsaturated ground

In this paper, a program of the finite element method (FEM), named as SOFT, using a finite element–finite difference scheme (FE–FD) for soil–water–air three-phase coupling problems, has been developed based on a rational and simple constitutive model for unsaturated soil proposed by Zhang and Ikariya (2011). In the program, similar to the works by Uzuoka et al. (2009) and Oka et al. (2010b), the FE–FD formulation in saturated condition of soil–water coupling problem, proposed by Oka et al. (1994), has been extended to unsaturated condition in soil–water–air fully coupling scheme, taking the saturation as a state variable. In order to verify the availability of the proposed numerical method, triaxial tests on unsaturated silty clay under fully undrained and unvented conditions, conducted by Oka et al. (2010a), are firstly simulated by the proposed method. The development of pore air pressure and pore water pressure measured in the specimen can be reproduced well by the proposed method. Furthermore, model tests on slope failure in unsaturated Shirasu, carried out by Kitamura et al. (2007), are also simulated by the same numerical method. From the simulation it is known that the slope failure behavior of the model ground observed in the tests can be described, on the whole, with satisfactory accuracy     

Coupling of smoothed particle hydrodynamics and finite element method for impact dynamics simulation

This paper presents an alternative method for coupling smoothed particle hydrodynamics (SPH) and finite element method (FEM) in a Lagrangian framework. The attachment and contact between SPH particles and finite elements are calculated. FE nodes are added to the SPH neighbor list for the attachment, and the continuity of the interface is guaranteed. The contact force on SPH particles and FE nodes is calculated with the same approach used in SPH particle to particle contact algorithm, and the identification of the contact surface and the surface normal is not required. Background particles are assigned in the position of FE nodes to facilitate particle approximation. The perforation of a cylindrical Arne tool steel projectile impacting a plate Weldox 460 E steel target is simulated in 3D to demonstrate the performance of the SPH-FEM coupling algorithm. The coupled computational model of viscoplasticity and ductile damage and Gruneisen EOS are used for the target plate. A particle-kill algorithm is used to invalidate the damage particles. Good agreement between the numerical simulations and the experimental results is obtained, and the ballistic limit velocity obtained from the SPH-FEM coupling algorithm gives a deviation of 2% from the experimental data.     

竖井冻结壁形成过程的光滑粒子法模拟

土体在冻结管作用下的冻结过程会涉及到相变潜热释放问题,准确描述冻结管周边的温度分布特征及冻结锋面移动规律对确定冻结壁的厚度和安全合理设计有重要意义。光滑粒子算法作为一种拉格朗日型无网格粒子方法以其独特的优势,已成功地应用于多种类型工程科学问题的求解。基于光滑粒子法编写了相应的计算程序并尝试着求解相变导热问题,通过一个简单的具有解析解的算例验证了其实用性和可靠性,从而给出求解此类问题的一种新的求解思路,并拓展了光滑粒子法的应用范围。最后针对煤矿井筒建设中冻结壁成形过程进行数值分析,计算了单圈等间距设置冻结管时的温度场的分布演化特征,比较了热物理性质不同的两种土体介质在相同冻结条件下的冻结效果,重点分析了采用不同交错布孔方案对冻结壁成形过程的影响,从而为工程设计提供一定的依据。     

Thermo-hydro-mechanical-air coupling finite element method and itsapplication to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.     

基于SPH粒子法的盲天井掏槽爆破数值模拟

针对上向盲天井掏槽孔爆破效果,运用补偿系数法对周边大空孔孔间距进行计算并进行方案制定,利用光滑粒子流体动力学方法(SPH粒子法)进行数值模拟计算,开展盲天井掏槽爆破周边空孔作用以及补偿系数对爆腔及岩石损伤范围影响研究。研究结果表明:在孔间距一定时,爆腔面积随补偿系数增大呈增加趋势;当补偿系数达到2.42时爆破效果最佳且达到峰值0.54 m²,而后爆破效果作用达到极限,爆腔面积变化趋于稳定;岩石损伤范围因炸药作用效果有限,总体变化范围在10%以内;模拟过程中SPH粒子能良好地模拟出爆破过程中岩石运动状态、空孔填充情况以及岩石损伤范围。所得模拟结果与现场试验爆腔断面面积吻合度高,说明数值模拟计算具有一定的准确性。     

基于预条件共轭梯度法的直流电阻率三维有限元正演研究

对直流电阻率法勘探而言,对其反演结果的精度和速度的要求越来越高,这就需要提出一套优化有限元数值正演速度和精度的计算方案。设计了系数矩阵的一维非零元素压缩存储模式,设置了索引数组以便按照行号和列号对元素进行索引,与变带宽存储模式相比,其内存占用量明显减小。为提高正演计算速度,利用预条件共轭梯度法（PCG）求解有限元中的大型稀疏线性方程组。在PCG法中,将雅可比迭代中的对角阵作为预处理矩阵,与其它预处理矩阵相比,其具有求逆方便、无需存储空间的特点,使得大型线性方程组的求解速度大大提高。另外,在直流电阻率三维正演中,采用了异常电位法,提高了电源点附近的解的精度。以二层地层的电阻率勘探为例,初步验证了计算方案的实用性。利用上述方案,重点对隧道含水断层的电阻率法超前探测进行了有限元数值正演,并进行了相应的物理模型试验。对比显示,数值正演结果与试验数据基本一致,且数值正演的速度和精度均显著提高。     

A simplified method for evaluating temperature effect on the behavior of layered soil with a time-varying cylindrical heat source

The engineering application of cylindrical heat source usually influences the characteristics of the surrounding soil and induces significant coupling responses of temperature, seepage and stress fields. This paper presents a numerical investigation into the thermo-hydraulic-mechanical (THM) coupling behavior of layered soils surrounding a cylindrical heat source by combining the analytical layer element method (ALEM) and the finite element method (FEM). The FEM is utilized to analyze the soil-cylindrical heat source interaction and the ALEM is used to obtain the fundamental solution of the layered soil. Then the THM coupling solution between the heat source and the soil is obtained by the simplified FEM-ALEM coupling method. Detailed validation against experimental result, and verifications against semi-analytical solution and numerical results by Comsol Multiphysics are performed to confirm the robustness of the present method, followed by extensive parametric studies to examine the effects of decaying half-life and type of the time-varying heat source, and the soil layered characteristics on the behavior of soils. It’s evident that the present method is accessible and can be implemented via common programming language, e.g. Fortran.