Geomaterials in general, and soils in particular, are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water. In the limit of zero compressibility of water and soil grains and zero permeability (which correspond to the classical 'undrained' assumption of Soil Mechanics), the functions used to interpolate displacements and pressures must fulfill either the Babuska-Brezzi conditions or the much simpler patch test proposed by Zienkiewicz and Taylor. These requirements exclude the use of elements with equal order interpolation for pressures and displacements, for which spurious oscillations may appear. The simplest elements with continuous pressures which can be used in 2D are the quadratic triangle and quadrilateral with linear and bilinear pressures, respectively. The purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures (T3P3) and bilinear quadrilaterals (Q4P4). The proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist.

提出用厚度较小的常规矩形（平面）或立方体（空间）单元来描述滑坡体与岩基之间的接触面，并给出了使滑动面上应力满足摩尔库仑极限条件的非线性迭代算法。在此基础上提出了保留滑动面上最下端单元处于弹性状态的滑坡体抗滑稳定安全系数的有限元迭代解法。这种方法可用于求解2维或3维问题，且能同时给出边坡临界失稳时的位移场和应力场。给出了具有折线滑动面的滑坡体抗滑稳定安全系数计算实例，结果表明该方法有效、合理和可靠。

本文提出了拱坝应力分析的有限元内力法，该法首先按常规方法建立拱坝及地基在水压力、自重等荷载作用下的有限元平衡方程，求解结点位移和单元应力，然后将坝体分解为拱系和梁系，根据拱和梁的内力平衡条件求解指定截面上的约束内力，并进而求解相应截面上的内力（弯矩、轴力、剪力等）和坝体内任一点的等效应力。文中推导了相应的计算公式，并通过对典型的圆筒拱坝和拟建的某高拱坝的应力分析说明了该方法的正确性。

本文对有限元内力法求解拱坝等效应力分析方法进行了进一步改进。建立了拱梁向应力为直线分布时以上、下游面等效应力为未知量而拱或梁截面上的约束内力为已知量的求解方程，并根据常规的多拱梁应力分布假定及上、下游面已知应力边界条件，导出了上、下游面其余应力分量求解公式。对溪洛渡高拱坝在水压力（含淤砂压力）、温升、温降及自重等荷载作用下不同网格的计算结果表明，拱厚方向采用两层以上单元、拱梁方向网格采用足够精度的网格可得到基本稳定的等效应力结果。

The accurate prediction of the behaviour of geostructures is based on the strong coupling between the pore uid and the solid skeleton. If the relativ e acceleration of the uid phase to the skeleton is neglected, the equations describing the problem can be written in terms of skeleton displacements (or velocities) and pore pressures. This mixed problem is similar to others found in solid and uid dynamics. In the limit case of zero perme-abilit y and incompressibility of the uid phase, the restrictions on the shape functions used to approximate displacements and pressures imposed by Babuska-Brezzi conditions or the Zienkiewicz-Taylor patch test hold. As a consequence, it is not possible to use directly elements with the same order of interpolationfor the eld v ariables. This paper proposes tw o alternative methods allowing us to circumvent the BB restrictions in the incom- pressibilit y limit, making it possible to use elements with the same order of interpolation. The rst consists on in troducing the divergence of the momentum equation of the mixture as an stabilization term, the second is a generalization of the tw o step-projection method introduced by Chorin for uid dynamics problems.