有自由面渗流分析的高斯点法

有自由面的渗流问题是比较复杂的非线性问题，这类问题的有限元求解一般采用固定网格法。本文根据饱和区和非饱和区的渗流特点，提出了高斯点法，该算法原理简单，易于实现。     

杂交边界点法求解带自由面的渗流问题

将杂交边界点法与迭代法相结合,求解有自由面的渗流问题。杂交边界点法基于杂交位移变分原理和移动最小二乘近似,利用基本解插值域内的场函数,而边界上的变量则用移动最小二乘近似,是一种纯边界类型的无网格方法。利用该方法只需在边界上布点而不需要划分任何网格的特性,先假定自由面的初始位置,再进行迭代求解。数值算例表明,该方法精度较高、计算量较小,适合于求解各种具有自由面的渗流问题。     

基于ABAQUS模拟渗流作用下的大坝浸润面分析

堰塞坝是由崩塌、滑坡等堵塞河道而形成的天然坝体。区别于人工坝,堰塞坝具有坝体结构松散、材料分布不均的特点,其一旦形成,极易在短时间内发生失稳破坏(漫顶溢流、渗流破坏及坝坡失稳),威胁下游群众的生命财产安全。堰塞坝的失稳破坏主要受到上游水位、坝体渗流及余震作用的影响,本文以唐家山堰塞坝为研究背景,基于通用有限元软件ABAQUS建立堰塞坝渗流及动力响应分析模型,研究堰塞坝在渗流及余震作用下的稳定性,并进一步分析渗流及坝体余震对堰塞坝溃坝模式的影响。研究结果表明,(1)唐家山堰塞坝坝体发生渗透破坏的可能性较小,但随着上游水位的上升,堰塞坝发生渗流破化的概率增大;(2)堰塞坝内部动力响应特征表现为沿坝高从上到下,坝体的加速度放大倍数逐渐减小,动力响应呈现明显的“表面放大”效应;(3)余震作用下,堰塞坝不会发生整体失稳破坏,但余震使得堰塞坝坝高降低,从而加速其发生漫顶溢流破坏。     

A variational inequality approach to free surface seepage in an inhomogeneous dam

The current work uses Baiocchi's transformation to obtain heuristically a formulation of the inhomogeneous dam problem. When finite element methods are applied the finite dimensional problem is a variational inequality which may be solved to obtain approximate solutions. The main advantage of the method is that it uses a fixed mesh. The finite dimensional problem is solved by means of succesive overrelaxation with projection. Although the standard convergence theory¹ for this method does not apply in this case, because the stiffness matrix is not symmetric, satisfactory and rapid convergence was obtained in all of our examples. Numerical results are given for some examples.     

岩土体渗流自由面问题的重心插值无网格方法

岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。     

三维非恒定渗流自由面边界积分项的高精度数值积分

在三维非恒定渗流有限元计算中,不可避免地需计算自由面上的边界积分项。建议一种高精度数值积分的方法求取自由面边界积分项。其基本思路是,基于8节点空间等参单元,根据压力为零的边界条件确定自由面满足的曲面方程,将自由面边界积分转化为ξη平面上的二重积分;然后再计算自由面与三维等参单元的交点,将交点投影到局部坐标平面ξη上,并根据点与线的相对关系,确定投影点所围成的局部坐标积分区域;再将总积分区域划分成若干个三角形子区域,并利用变步长Simpson方法计算各三角形子区域上的二重积分,从而实现了高精度的自由面边界积分。该方法避免了单元中自由面为平面的假设,可提高计算精度,特别对于单元内自由面变化剧烈情况,更为显著。将该方法应用于砂槽模型和土坝的渗流分析中,计算结果与实际情况较为接近。     

改进的有自由面渗流问题的Bathe算法

建议了一个新的有自由面渗流问题的变分不等式提法,该提法通过将潜在出渗面上的边界条件提为Signorini型条件,从而从理论上消除了出渗点的奇性,解决了出渗点的定位问题。同时在离散求解时,通过引进依赖于网格参数的连续型Heaviside函数,克服了Bathe算法中所固有的网格依赖性,提高了这类方法的数值稳定性。     

An approximate analysis procedure for piled raft foundations

A piled raft foundation comprises both piles and a pile cap that itself transmits load directly to the ground. The aim of such a foundation is to reduce the number of piles compared with a more conventional piled foundation where the bearing effect of the pile cap, or raft, is ignored. This paper describes a ‘hybrid’ approach for the analysis of piled raft foundations, based on a load transfer treatment of individual piles, together with elastic interaction between different piles and with the raft. The numerical analysis is used to evaluate a simple approximate method of estimating the overall response of the foundation from the response of the component parts. The method leads to estimates of the overall foundation stiffness, the proportion of load carried by the pile group and the raft, and an initial assessment of differential settlements. Parametric studies are presented showing the effect of factors such as raft stiffness and pile spacing, length and stiffness, and a worked example is included demonstrating the accuracy of the approximate design approach.     

有自由面渗流分析的三维数值流形方法

提出了求解有自由面渗流问题的三维数值流形方法,通过构造任意形状流形单元的水头函数,推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程,并给出了自由面的迭代求解策略和渗透体积力的计算方法。典型算例的数值分析表明,该方法采用数学网格覆盖整个材料区域,在自由面的迭代求解过程中数学网格保持不变,只考虑自由面以下渗流区的介质,只对自由面以下的流形单元形成总体渗透矩阵,具有精度高、收敛速度快、编程简单等优点,而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力,因此,特别适用于有自由面渗流问题的模拟。     

An approximate numerical analysis of pile–raft interaction

This paper presents an approximate method of numerical analysis of piled–raft foundations in which the raft is modelled as a thin plate and the piles as interacting springs of appropriate stiffness. Allowance is made for the development of limiting pressures below the raft and of the ultimate axial load capacity of the piles. Comparisons between this analysis and existing solutions verify that, despite the approximations involved, the analysis can provide solutions of adequate accuracy for the settlement and pile load distribution within a piled raft. Comparisons are also made with the results of a series of centrifuge tests and with measurements of the performance of a full-scale piled raft. In both cases, the analysis predicts very well the settlement and proportion of load carried by the piles.     

无压渗流分析的复合单元法

针对无压渗流问题,在传导矩阵调整法的基础上,对穿越自由面的单元用复合单元来处理,每个复合单元具有两套结点水头,一套用于饱和区的水头插值;另一套则用于无水区。通过变分原理,推出了控制方程并在程序中实现。应用复合单元法可以较好地解决自由面的插值问题,消除了穿过自由面单元的水上部分对自由面附近结点水头的贡献,同时对逸出面边界条件的处理也更加方便和准确。算例表明了该方法的有效性。     

F. E. analysis of field consolidation curves obtained with the modified borehole shear device (BHSD)

A modified version of the bore hole sheat device (BHSD) was used to obtain field consolidation curves in a soft sensitive clay. The Porewater pressure dissipation was monitored at the centre of one of the shear plates. This paper describes briefly the in situ device employed and demonstrates the basic features of the linearelastic F. E. program ‘SOL’. A detailed study is made to simulate the field behaviour with the finite element approach. Comparisons are made between the field and analytical consolidation behaviour. Difficulties in predicting the value of the coefficient of consolidation of a sensitive clay using the BHSD consolidation curves are discussed.     

Conformal analysis of seepage below a hydraulic structure with an inclined cutoff

Conformal mapping techniques are used to obtain an exact solution for seepage flow below a hydraulic structure founded on permeable soil of infinite depth for a flat floor with an inclined cut-off at the downstream end. Results are presented for different values of b/s and θ. The exit gradient decreases considerably along a distance beyond the floor end with an increase in cut-off inclination. The maximum exit gradient decreases for θ = 10, 20 and 30° and starts increasing for θ = 45°. The uplift pressure decreases as θ increases. It is concluded that using an inclined cut-off increases the factor of safety in design against uplift and piping.     

Stochastic analysis of free surface flow through earth dams

This research investigated the unconfined flow through dams. The hydraulic conductivity was modeled as spatially random field following lognormal distribution. Results showed that the seepage flow produced from the stochastic solution was smaller than its deterministic value. In addition, the free surface was observed to exit at a point lower than that obtained from the deterministic solution. When the hydraulic conductivity was strongly correlated in the horizontal direction than the vertical direction, the flow through the dam has markedly increased. It is suggested that it may not be necessary to construct a core in dams made from soils that exhibit high degree of variability.     

An approximate analytical solution for calculating ground surface settlements due to diaphragm walling

This paper focuses on the derivation of an approximate analytical solution to predict ground surface settlements along the centre-line perpendicular to a slurry-supported diaphragm wall panel. An analytical model of trench excavation is constructed by applying linearly-distributed total earth pressure changes on the sidewalls and the base of the trench in a homogeneous, isotropic, elastic half-space. By applying the principle of superposition appropriately, an explicit solution to calculate ground surface settlements is derived by integrating Mindlin’s displacement formulae. The validity of the solution is verified by three-dimensional finite-element analyses and case studies. Based on the results obtained from a parametric study using the newly derived solution, an algebraic formula is obtained as a first approximation for calculating ground surface settlements.     

不透水地基上均质土坝渗流自由面的有限元计算

为了保证土坝安全,水利工程中需要对土坝进行渗流计算,首先需要确定自由面。根据达西定律和渗流连续方程,以及水头和流量边界条件,建立了不透水地基上的均质土坝渗流的计算模型。利用Geoslope软件,采用有限元离散的方法计算了土坝的渗流自由面,并分析了土坝在不同的渗透系数情况下的自由面位置的差异。最后,解析解计算的自由面结果验证了有限元计算自由面方法是正确的。     

Rock nail reinforcement of a free surface

Rock nailing of the surface instability test specimen is considered as a means to reinforce the rock and increase its free surface strength (FSS). This technique is modeled using Cox's original shear‐lag method. In the continuum sense, nail reinforcement is modeled as a body force that acts as a confinement. Results are presented for a single nail in a surface instability test specimen and for a nail‐reinforced test specimen with a given nail density. The results show that nail length and the nail–rock contact modulus are important parameters. The effect of nail reinforcement increases with the second power of nail length. Rock dilation is also important since the action of the nails is mobilized from the difference in displacement between the rock and the nail. The results show the potential for a significant increase in the FSS of the rock. Copyright © 2011 John Wiley & Sons, Ltd.     

用空气单元法求解渗流场的逸出边界问题

依据空气单元模拟排水孔的思路,在渗流场任意可能逸出边界外布置一层渗透性较强的单元,与其他实体单元一起进行渗流计算,可以实现该边界的自动求解。与现行方法相比,不仅省去了逸出边界迭代计算的麻烦,而且避免了由于逸出点定位不准确而可能引起的渗流计算不合理或收敛困难等缺陷。算例分析表明,空气单元法的计算精度与空气单元的相对渗透系数R有关,与厚度L无关。当选取了合适的R值后,可以较好地逼近现行方法。对于因引入空气单元而造成的强弱透水介质界面处数值拟真性差的现象,还提出了加入接触面薄层单元的改进方法。方法改进后,计算精度可进一步提高。最后,以小湾水电站22#坝段渗流场计算为例,说明该法的实用性和可行性。     

考虑饱和-非饱和渗流的土坡极限分析

给出了均质土坝的下游坝坡的安全系数的计算方法。均质土坝的下游坝坡有可能会通过滑裂面发生破坏。土坝中的土坡通常处于非饱和状态。非饱和土坡的安全系数计算需要考虑吸力对抗剪强度的贡献以及土坡中的非饱和渗流。给出处于饱和-非饱和渗流状态下的土坡的安全系数,有助于评价均质土坝的安全系数。下游坝坡的安全系数计算方法有：极限平衡法、上限解法和下限解法,该算法适用于非饱和土坡,且是在饱和土坡安全系数的计算方法上修正得到的。算例中非饱和土坡安全系数的计算考虑了吸力对抗剪强度的贡献。考虑非饱和渗流理论的土坡安全系数计算方法通常更加接近现场实际情况,并且对于同一坝坡,考虑非饱和渗流计算出的土坡安全系数要比饱和渗流理论计算出的安全系数大。