Bearing capacity of shallow and deep foundations on rock mass : analytical and experimental investigations

It is well known that, except for potential installation problems, most rock masses are excellent and trouble-free foundation materials. A significant economy can be therefore realized in design if the foundation can be constructed on or in the surface or near-surface rock. Nevertheless, the construction of challenging structures with usually high loads and special requirements on rock foundations, have made it necessary to determine the bearing capacity of rock media accurately. It is within this framework that the present research was carried out. This dissertation provided analytical solutions for bearing capacity problems of both shallow and deep foundations resting on or in a rock mass that obeys the Hoek and Brown failure criterion. Considering the strip footing problem, improvements were brought by incorporating a non-associated flow rule in the plane strain upper bound limit analysis technique and analysing its effects on failure mechanisms and bearing capacity values. By assuming a rigid strip footing resting on a rock mass obeying the generalized Hoek and Brown failure criterion, the upper bound estimate for the bearing capacity was derived by preserving exactly the original nonlinear criterion. The multi tangential method was used to handle non-linear strength criterion issues. Furthermore, a sufficiently significant but conveniently simple formulation of a non-constant dilatancy angle model was derived. Closed-form expressions of the maximum resistance work rate were developed in any virtual velocity field. For practical purposes in rock engineering, tables and charts allowing easy and accurate estimates of the bearing capacity factor 0 were provided. The effect of the flow rule on 0 was carefully examined using different dilatancy parameters. To investigate the efficiency of the proposed solution, a series of static penetration tests of small-scale model footings (strip and circular) laying on a highly porous calcarenite rock mass was conducted. A reduction factor defined as the ratio of the measured acceptable bearing capacity to ultimate theoretical one was introduced. This factor reflects by how much should the theoretical bearing factor reduced to get an acceptable value of bearing capacity. It was suggested to estimate values as a function of the rigidity index and the friction angle of the rock mass. As for the bearing capacity of the pile foundation, an analytical calculation procedure was proposed to predict the shaft resistance for piles drilled to some depth into a rock layer. The developed solution requires a numerical integration over the embedment depth. Thus, for practical purposes, design charts, as well as an approximate solution, were provided allowing easy and accurate estimates of the average shear resistance. Results obtained from developed solutions were in excellent agreement when compared to published analytical results and very close to finite element analysis results. Moreover, this analysis procedure offered reasonable results when compared to field test measurements. Furthermore, and always within the framework of pile foundation, an analytical solution based on the cavity expansion theory was proposed for computing the bearing capacity at the tip of a pile embedded in rock mass obeying the H-B failure criterion. The pile end bearing capacity was evaluated by assuming that the pressure exerted at the boundaries of a pressure bulb immediately beneath the pile tip is equal to the limit pressure required to expand a spherical cavity. Besides, a relationship was derived to predict the pile load-settlement response. To demonstrate the applicability of the presented solution, the results of the present work were compared to those of 91 field tests from technical literature. Despite some limitations, it was found that the computed end bearing resistance was in good agreement with the measured field test results.(FSA - Sciences de l'ingénieur) -- UCL, 202

Cavity Expansion in Rock Masses Obeying the “Hoek–Brown” Failure Criterion

A unified approach is presented for the analysis of the expansion of both cylindrical and spherical cavities in an infinite elastic–perfectly plastic “Hoek–Brown” (H–B) material. The H–B failure criterion expressed in scaled form is adopted with a plastic flow rule characterized by a constant dilatancy angle ψ . Closed-form expressions are given for the extent of the plastic region and the related stress. Solutions of the displacement field in the plastic region are provided based on both small-strain and large-strain theories. An original relationship between the cavity pressure and its expansion is derived. The developed closed-form solutions are validated employing the finite element method. For comparison purposes, an approximate solution is presented by neglecting the elastic strains in the plastic region which reveals that the assumption of no elastic strains does not influence the results for strong rocks in contrast with weak rocks. For practical purposes, design charts are provided allowing easy and accurate estimates of the limit pressure for cavity expansion in rock masses. The cavity expansion solution is finally validated against results obtained using the Finite Element modelling

Pile end bearing capacity in rock mass using cavity expansion theory

Much empiricism is involved in design of rock-socketed piles in rock masses. In light of this, an analytical solution based on the cavity expansion theory is proposed for calculating the ultimate bearing capacity at the tip of a pile embedded in rock masses obeying the Hoek-Brown failure criterion. The ultimate end bearing capacity is evaluated by assuming that the pressure exerted at the boundaries of a pressure bulb immediately beneath the pile tip is equal to the limit pressure required to expand a spherical cavity. In addition, a relationship is derived to predict the pile load-settlement response. To demonstrate the applicability of the presented solution, the results of this study were compared to those of 91 field tests from technical literature. Despite the limitations, it is found that the end bearing resistance computed by the present work is in good agreement with the field test results

End bearing response of open-ended pipe piles embedded in rock

Prediction of bearing capacity of steel pipe piles in rock masses is an important consideration in civil engineering especially as such prediction influences the safety of the supported superstructures as well as the pile integrity in pile driving operations. Provided that the rock mass is described as a linear elastic and perfectly plastic material obeying the Hoek-Brown failure criterion, a finite element analysis is performed to investigate the embedment depth effect on the annular base bearing capacity and the failure mechanism of typical open-ended pipe piles in sedimentary rock masses. The pipe pile has smooth walls and rough toe surface. Annular toe resistance of pipe piles can serve as an estimate of the rock mass resistance to driving in a fully coring mode which is usually expected for large diameter open-ended pipe piles. Pipe pile results are also extended to circular piles and embedded strip foundations socketed in rock masses. The analysis is shown to highlight the influence of the annular geometry of the pipe pile causing an unsymmetrical failure mechanism with respect to pipe wall center as well as an inclination of rock mass reaction, which if sufficiently large, may lead to pile convergence and damage during pile driving operations. The failure mechanism legitimates the plug tendency to rise up in the pipe and explains the plug formation. The study demonstrates that in most practical applications, the bearing capacity of pipe piles approaches a limiting value, which is less than or at most equal to the end bearing capacity of an embedded strip foundation of width equal to the pipe wall thickness. A comparison has been made with experimental data. It is shown that the results are relatively in good agreement with test data in terms of rock mass resistance and the mechanism of rock plug formation

Cavity expansion analysis in elastic – brittle plastic rock mass

A comprehensive approach is presented for the analyses of both cylindrical and spherical cavity expansion in an infinite elastic – brittle plastic rock mass. The rock mass obeys the nonlinear generalized “Hoek – Brown” (H-B) failure criterion which is expressed in a scaled form. A plastic flow rule characterized by a constant dilatancy angle is adopted. Closed-form solutions are presented for the extent of the plastic region and the distribution of radial and circumferential stresses. For the displacement field, solutions in the plastic region are developed based on small strain theory. Finally, the solutions are validated using the finite element method

Bearing capacity of surface foundations resting on Hoek – Brown materials using equivalent Mohr – Coulomb parameters

Estimating the bearing capacity of surface foundations resting on rock masses is a necessary first step in the design of critical infrastructures. Although it is known that the rock masses behave nonlinearly according to the Hoek – Brown (H-B) failure criterion, there has long been a tendency to model rock failure as a linear Mohr – Coulomb (M-C) law for which extensive literature is available in terms of the foundation ultimate bearing response. This has provided an impetus for practicing engineers to find equivalent friction angle and cohesion so that the classical bearing capacity relationships can be used. This paper provides specific guidance for selecting equivalent M-C parameters to compute bearing capacity of surface foundation resting on rock masses. Numerical models validate that the suggested equivalent M-C parameters values result in bearing capacity values practically equal to those of the H-B material.L’estimation de la capacité portante des fondations superficielles reposant sur un massif rocheux est une étape primordiale dans la conception d’infrastructures. Bien que l’on sache que la roche atteint la rupture selon le critère non linéaire de Hoek – Brown (H-B), il existe depuis longtemps une tendance à la modélisation des massifs rocheux en tant que matériau linéaire Mohr – Coulomb (M-C) pour lequel une littérature abondante est disponible. Cela a incité les ingénieurs praticiens à trouver un angle de frottement et une cohésion équivalents, de sorte que les relations de capacité portante classiques puissent être utilisées. Ce document fournit des instructions spécifiques pour la sélection de paramètres M-C équivalents pour le calcul de la capacité portante des fondations superficielles reposant sur un massif rocheux. Des modèles numériques attestent que les valeurs des parameteres M-C équivalents ainsi suggérées produisent des valeurs de capacité portante pratiquement égales à celles résultant du critère H-B