A previous paper studied the stability of soldier-pile walls in clay under vertical loading using upper bound analyses. A classical Tresca yield criterion was assumed in that analysis. This paper extends that study by considering a tension truncated Tresca yield criterion in an upper bound numerical analysis of the problem. It shows that assuming zero tension soil strength has a significant influence on the values of the minimum soldier-pile resistance required to ensure stability.
A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.
The paper describes the three-dimensional numerical implementation of the Lade-Duncan criterion in a finite element limit analysis (FELA) code. Validation is done using examples with a known solution. To conclude the proposed numerical tool is applied to the calculation of the ultimate bearing capacity of square footing.
A strict upper-bound limit analysis finite element formulation is used to estimate shape factors s_gamma and s_q for determining the bearing capacity of shallow foundations using the classic bearing capacity formula. The finite element formulation uses a quadratic approximation for the velocity field, an extension of a previously published Augmented Lagrangian formulation with a linear velocity field, and was implemented for a parallel processing environment. Results from determining the limit loads under three-dimensional conditions are presented and compared with previously published data. The results obtained allow a strict upper-bound determination of the shape factors. Furthermore, a practical proposal for these factors is made and compared with other proposals made by other authors.
This paper deals with the determination of upper and lower bounds for the three-dimensional undrained stability of shallow tunnels. The tunnel is circular and a distance between its face and its lining is considered. The soil shear strength is modeled using the Tresca criterion. Results of the upper and lower bounds of the stability number are presented, for several geometrical and resistance configurations and their comparison with previous results is made, showing the clear improvement obtained. Finally, equations approaching the stability number are proposed.
The vertical stability of anchored concrete soldier-pile walls is highly influenced by the complexity of the interaction between the different parts of the structure, i.e., wall, anchors, and supported soil mass. The problem is analyzed using upper bound limit analysis through published solutions and proposed closed-form equations. A comparison is made between these equations and numerical limit analyses. An estimate of the theoretical minimum pile resistance required to avoid excavation collapse is presented. Published finite element elastoplastic results are used for comparison.Key words: anchored retaining wall, concrete soldier-pile walls, vertical equilibrium, finite elements, limit analysis, soil-to-wall interface shear forces.
This paper aims at contributing towards a better understanding of the non-uniform elastoplastic torsion mechanism of I-section beams. The particular case of cantilevers subjected to an end torque is analysed, which constitutes a simple yet interesting problem, since the maximum torque is very close to the so-called Merchant upper bound (MUB), with added independent maximum bishear and Saint-Venant torques. Consequently, it turns out that the maximum torque can be significantly higher than that for uniform plastic torsion. Besides the MUB, several solutions are presented and compared, namely (i) a stress resultant-based solution stemming from the warping beam theory differential equilibrium equation and (ii) solutions obtained with several beam finite elements that allow for a coarse/refined description of warping. It is found that all models are in very close agreement in terms of maximum torque (including the MUB) and stress resultants. However, the beam finite elements that allow for bishear, even with a simplified warping function, are further capable of reproducing quite accurately the stress field, as a comparison with a 3D solid finite element solution shows. Although the paper is primarily concerned with the small displacement case, the influence of considering finite rotations is also addressed.
A numerical implementation of the upper-bound theorem of limit analysis is applied to determine two-dimensional (2D) and three-dimensional (3D) active horizontal earth pressure coefficients considering seismic actions through a horizontal seismic coefficient. Results are obtained for vertical wall, horizontal soil, different friction angles of the soil, soil-to-wall friction ratios, horizontal seismic coefficients and wall width-to-height ratios. The few cases for which 3D active earth pressure coefficients are available in the literature using upper-bound methods were used for comparison with the corresponding earth pressure coefficients obtained in this study. This showed a general improvement of these results, which allows expecting a good accuracy for the set of cases studied. The ratios between the 3D and 2D horizontal active earth pressure coefficients are found to be practically independent of the soil-to-wall friction ratio. An equation is proposed for calculating these ratios. This equation can be easily used in the design of geotechnical structures requiring the determination of 3D active earth pressure coefficients.
The Hoek–Brown failure criterion has been widely applied to predict the strength of rock masses, demonstrating its relevance in diverse geotechnical contexts. This paper presents a novel 3D numerical implementation of the Hoek–Brown criterion in a finite-element limit analysis code. The proposed formulation is unique in its ability to produce strict upper and lower bounds for 3D problems, providing more accurate and reliable predictions of failure mechanisms compared to previous formulations. The validity of the formulation is demonstrated through comparisons with known analytical solutions or other authors’ numerical solutions. Furthermore, the proposed numerical tool is used to determine the stability of shallow circular tunnels in rock masses, highlighting its practical applicability in engineering design.
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