International Journal of Geomechanics

This paper presents three plasticity models that can be applied to numerically simulate pipe–soil interaction. They can be applied individually to evaluate the force–displacement response of a small plane-strain pipe section or in combination to simulate a long pipeline system. In the latter, numerous pipe–soil elements are attached to structural finite elements, each simulating localized foundation restraint along the pipeline. The three models are increasing in sophistication, mainly due to the manner in which they account for the behavior within an allowable combined loading surface. The first is based on traditional strain-hardening plasticity theory and therefore assumes a purely elastic response inside a single expandable yield surface. The second allows some plasticity due to the use of a bounding surface, and the third accounts for kinematic hardening through the introduction of a second smaller surface. The models are detailed in this paper, allowing for simple numerical implementation. Importantly, they are incorporated within the structural analysis of a pipeline and their potential to investigate generic pipeline system behavior is demonstrated. The applicability of the three models is interpreted theoretically and their differences shown through application for (1) a one pipe–soil interaction element and along (2) a $100\mathrm{m}$ segment of pipeline. The latter shows the practical application of these models to offshore pipeline engineering examples, with the influence of a free span behavior investigated. The ability to model complex cyclic loading is also shown.

The engineering design of shallow foundations on sand is almost universally based on one of the variants of the classical bearing capacity formula. However, this formula is suitable only where the sand exhibits dilative behavior and a clear rupture mechanism forms at failure. The main challenge then is choosing a suitable friction angle, taking into account the soil density and the high stresses beneath the footing. When other conditions apply, in particular when the footing is large or founded on compressible materials, alternative approaches need more focus on soil compressibility. Two simple semianalytical formulas are proposed and explored in this paper: (1) an analysis using a one-dimensional (1D) compression equation; and (2) an analysis using the concept of “bearing modulus.” It is argued that the bearing modulus approach may be used for conditions that reflect moderate design parameters (i.e., moderate foundation size and sand compressibility), but for very large foundations or highly compressible soils the 1D compression method is found more suitable. It is shown that the bearing modulus analysis can be approached in terms of the compression response of the soil, suggesting a possible route to link the bearing modulus directly to the compression model parameters of the soil.

In this paper, an approach for reliability-based design optimization of reinforced concrete cantilever retaining wall is described. A parametric study is conducted to assess the effect of uncertainties in design parameters on the probability of failure of cantilever retaining walls. In total, ten modes of failure are considered, viz. overturning of the wall about its toe, sliding of the wall on its base, eccentricity, bearing capacity failure below the base slab, and shear and moment failure in the toe slab, heel slab, and stem. The analysis is performed by treating backfill and foundation soil properties, geometric properties of wall, and reinforcement and concrete properties as random variables. These results are used to develop a set of reliability-based design charts for different coefficients of variation of friction angle of backfill soil (5 and 10%) and targeting reliability index $\left({\beta }_t\right)$ in the range of 3–3.2 for all failure modes. A comparative study is also presented, which shows that optimized sections have less areas of cross section compared to those obtained from specifications on dimensioning of retaining walls available in literature.

This paper shows that for perfect plasticity, the closest point projection method (CPPM) and the cutting plane algorithm (CPA) for return mapping are exactly equivalent for piecewise linear yield criteria under both associated and nonassociated plastic flow. The paper demonstrates this by presenting closed-form expressions for returned stresses in terms of predicted stresses. A consequence of this exact approach is that the final stresses can be obtained in a single iteration. The equivalence of CPPM and CPA is further demonstrated numerically by comparing five previously published algorithms for return mapping to Mohr–Coulomb in a finite-element analysis of bearing capacity. The analyses also highlight issues relating to singularities that occur at the corners of the Mohr–Coulomb surface. It is shown that many of these problems can be avoided if the return mapping is performed in principal stress space as opposed to general stress space.

An implicit integration algorithm has been refined to predict the stress–strain–strength response of unsaturated soil under suction-controlled, multiaxial stress paths that are not achievable in a conventional cylindrical cell. The algorithm supports numerical analyses in a deviatoric plane by using a mixed control constitutive driver, in conjunction with a generalized Cam-Clay model that also incorporates the influence of a third stress invariant, or Lode-angle $\theta$ , within a constant-suction scheme. True triaxial data from a previously accomplished series of suction-controlled triaxial compression, triaxial extension, and simple shear tests on 10-cm cubical specimens of silty sand, were used for the tuning and validation of the refined algorithm. The elliptical Willam–Warnke surface was adopted for simulation of unsaturated soil response in three-invariant stress space. Reasonably satisfactory agreement was observed between experimental and predicted deviatoric stress versus principal strain response for different suction states, as well as between experimental and predicted strength loci in a deviatoric plane.