P. de Buhan

On the validity of the effective stress concept for assessing the strength of saturated porous materials: A homogenization approach

Abstract The much debated question of whether the strength criterion of a fluid saturated porous medium, such as most geomaterials, can be expressed in terms of “effective stress,” is critically examined in this paper using the yield design homogenization theory as an investigating tool. Adopting a periodic description of the saturated porous material at the microscopic level, where the fluid phase exerts a pressure on the solid matrix making up the skeleton, a general definition of the strength properties of the porous material at the macroscopic scale is given. While some situations are identified where the “effective stress principle,” as classically formulated, remains appropriate, it is proved that for a frictional solid matrix, such a principle, even in its generalized form, is not relevant. Nevertheless, the dependence on the pore pressure can still be specified in a simple way, so that the complete knowledge of the criterion for any prescribed value of the pore pressure only requires determining the strength properties of the dry porous material. Moreover, the possibility of adopting sufficiently accurate approximations of the actual criterion by resorting to an effective stress formulation is discussed.

A multiphase constitutive model of reinforced soils accounting for soil-inclusion interaction behaviour

A two-phase continuum description of reinforced soil structures is proposed in which the soil mass and the reinforcement network are treated as mutually interacting superposed media. The equations governing such a model are developed in the context of elastoplasticity, with special emphasis put on the soil/reinforcement interaction constitutive law. As shown in an illustrative example, such a model paves the way for numerically efficient design methods of reinforced soil structures.

Face stability of shallow circular tunnels driven under the water table: a numerical analysis

The stability analysis of a tunnel excavated in a water-saturated frictional soil is investigated in the light of a failure design approach. The soil strength properties being classically formulated in terms of effective stresses, it is first shown how the effect of seepage flow generated by the excavation process, may be accounted for in such an analysis by means of driving body forces derived from the gradient of an excess pore pressures distribution. The latter is obtained as the solution of a hydraulic boundary value problem, in which both water table evolution and soil deformability can be neglected. A variational formulation of this hydraulic problem in terms of filtration velocities is then presented, leading through appropriate numerical treatment, to a search for the minimum without constraints of a quadratic functional (hybrid formulation), which is formulated by a finite element method. Some numerical examples are given, which provide ample evidence of the crucial role played by seepage forces in the tunnel face stability, since the factor of stability may be divided by as much as three. The influence of such parameters as the tunnel relative depth or soil anisotropic permeability is finally discussed, thus offering a first illustration of the various capabilities of this numerical tool. Copyright

A Micromechanics-Based Approach to the Failure of Saturated Porous Media

This contribution is devoted to the implementation of a homogenization method for deriving the strength or failure properties of a fluid-saturated porous medium, from those exhibited by its individual constituents at the microscopic level. Within this context, a specific attention is paid to the possibility of adopting an effective stress formulation. While the case of a purely cohesive solid matrix provides the first illustrative example where the ‘effective stress principle’ as originally stated by Terzaghi is fully applicable, the analysis is then particularly focused on porous sandstones, modelled as periodic packings of cemented rigid grains. A closed-form analytical expression is thus obtained for the strength criterion of such rock materials, which proves to be a function of a generalized effective stress formed as a linear combination of the total stress and the pore pressure, as in the case of poroelasticity. It is shown in particular that the key microstructural parameter involved in this formulation is the ratio between the intergranular contact area and the grain cross-section area. A possible extension of the homogenization procedure in order to account for a still more realistic description of the sandstone microstructure is finally outlined.

Influence of a soil-strip interface failure condition on the yield-strength of reinforced earth

Abstract A comprehensive approach to the yield-strength of reinforced earth when considered as a macroscopically homogeneous material is presented within the framework of both the yield design and homogenization theories. In this paper, a more specific attention is paid to the case when a failure condition relating to the interfaces between the soil and the reinforcing strips has to be taken into account. A closed form expression of the corresponding macroscopic strength criterion of reinforced earth is given, along with a geometrical interpretation in the space of stresses. The analysis clearly shows a significant reduction in the overall strength of reinforced earth when compared to the case of perfect bonding. The consequences of such a reduction on the stability of some typical reinforced soil structures are then carefully examined by means of the yield design kinematic method using ⪡rigid blocks⪢ failure mechanisms.

Mixed modelling applied to soil–pipe interaction

Abstract This paper presents a simplified approach to the study of a pipe in a geotechnical context of landslide motion. The mechanical description of the different components, the pipe and the soil, is made within the framework of the so-called “mixed modelling approach” previously used for dealing with reinforced soil structures. Upper bound estimate of non-dimensional weight loading parameter is obtained by making use of the yield design kinematic method. The class of virtual motions considered is a three-dimensional rotational failure mechanism for the slope and the pipe system. Application of the approach are presented and discussed with emphasis on identifying and optimizing some of the important factors that control the integrity of the pipe. Several conclusions are drawn regarding the pipe-slope stability problem, that of prime importance being the size of the pipe.

A variational approach-based method for simulating the post-liquefaction behaviour of soil masses

Publisher Summary This chapter proposes a general numerical scheme aimed at stimulating the evolution of a soil subject to a liquefaction phenomenon, the constitutive behavior of which is described by means of a regularized Bingham model. This procedure is based on the combination of a variational principle for the velocity field and a step-by-step time integration algorithm making it possible to follow the geometry changes. A first illustration of the method implemented in a finite element code is also presented in the chapter. The adoption of a Bingham model instead of a Newton model for describing the behavior of the liquefied soil results in increasing the soil resistance and thus limiting the amplitude of geometry change of liquefied soil spreading. Some hypotheses, such as the prefect bonding assumption between the liquefied soil and the substratum can be investigated and replaced by a more realistic boundary condition allowing for possible slippage beyond a certain shear stress level.

Application of the Yield Design Theory to the Mechanics of Reinforced Soils

The considerable development of various reinforcement techniques in soil mechanics over the last few decades, has made it necessary to devise both reliable and efficient methods for analysing the stability of such composite soil structures. The Yield Design theory is perfectly well suited to undertaking such a task, since it provides a comprehensive mechanical framework. The purpose of this contribution is to present two different approaches to the problem.

Stability analysis of reinforced soil structures through a homogenization method

The increasing use of soif reinforcement techniques in the field of geotechnical engineering, requires the elaboration of reliable as weil as practical yield design procedures for reinforced soif structures. The method presented hereafter, originates from the intuitive idea that from a macroscopic point of view, reinforced soils can be regarded as homogeneous but anisotropie materials, on account of the existence of privileged orientations due to the reinforcing inclusions. The strength criterion of such an equivalent homogeneous material can be theoretically determined starting from the strength characteristics of the reinforced soif components. Application of such a criterion, which can be explicitely formulated within the framework of a multilayered modelization for the reinforced soil, is then performed on the case of the stability analysis of sorne typical structures. Special concern has been given to reinforced earth structures, and it turns out that the theoretical estimations so obtained are in good agreement with experimental data. Despite sorne limitations which are outlined in the paper, the yield design homogenization procedure thus proposed is likely to become an appropriate design method for reinforced soif structures. * École Polytechnique, 91128 Palaiseau Cedex.

Numerical Yield Design Analysis of High-Rise Reinforced Concrete Walls in Fire Conditions

The present contribution aims at developing a numerical procedure for predicting the failure of high rise reinforced concrete walls subjected to fire loading conditions. The stability of such structures depends, on the one hand, on thermal strains inducing a curved deformed configuration and, on the other hand, on a local degradation of the constitutive material strength properties due to the increase of temperature across the wall thickness. A three step procedure is proposed, in which the yield design (limit analysis) method is applied on two separate levels. First, an up-scaling procedure on the wall unit cell is considered as a way for assessing the generalized strength properties of the curved wall, modelled as a shell, by taking into account reduced strength capacities of the constitutive materials. Secondly, the overall stability of the wall in its fire-induced deformed configuration is assessed using lower and upper bound based on shell finite elements and the previously determined temperature-dependent strength criterion. Second-order cone programming problems are then formulated and solved using state-of-the-art solvers. Different illustrative applications are presented to investigate the sensitivity of the wall stability to geometrical parameters. Finally, the influence of imperfect connections between panels is also considered using a simple joint behaviour.