Undrained Bearing Capacity Research Articles

Limit analysis of the undrained bearing capacity of offshore pipelines

The ultimate bearing capacity of a rigid, plane-strain pipe segment embedded in undrained clay is studied using numerical limit analysis. The pipe is considered to be ‘wished in place' at invert penetrations ranging from zero to five pipe diameters, thus providing coverage of both on-bottom (partially embedded) and trenched (fully embedded) offshore pipelines. The soil is modelled as a rigid-plastic Tresca material with either uniform strength or strength proportional to depth. The effects of soil weight, interface roughness and interface tensile capacity are investigated in a systematic manner. All calculations are performed using the finite-element limit analysis code OxLim, which uses adaptive mesh refinement to compute tightly bracketed lower- and upper-bound plasticity solutions. The velocity fields from the upper-bound analyses provide the corresponding failure mechanisms. The paper initially focuses on purely vertical loading (penetration and uplift), and then addresses combined vertical and horizontal loading. A comprehensive set of design curves and failure envelopes is presented, with the results explained in terms of the changing failure mechanisms. These results are immediately applicable in practice. In particular, current industry-standard procedures for design against pipeline upheaval are critically reviewed, and are shown to have potentially unconservative shortcomings.

Effect of spatial variability on the bearing capacity of cement-treated ground

This paper presents a reliability assessment for the undrained bearing capacity of a surface strip foundation based on the results of a probabilistic study in which the shear strength and unit weight of cement-treated ground are represented as random fields in Monte Carlo simulations of undrained stability using numerical limit analyses. The results show how the bearing capacity is related to the coefficient of variation and correlation length scale in both shear strength and unit weight. Based on the results, the authors propose an overdesign factor, tolerable percentage of defective core specimens, and resistance factors for LRFD ultimate limit state of surface footings on cement-treated ground in order to achieve a target reliability index and probability of failure. The proposed method is illustrated through example calculations based on the spatial variation of unconfined compressive strength measured using a variety of cement-mixing methods from projects in Japan.

Undrained Bearing Capacity of Deeply Buried Flat Circular Footings under General Loading

Estimation of a footing’s bearing capacity under general loading is a topic of wide interest, especially for the offshore energy industry. Although there have been several studies in the past few decades on shallow footings under general loading, limited work has been done for deeply buried footings. This paper presents results of a numerical investigation into the undrained bearing capacity of deeply buried flat circular footings in clay of both uniform and linearly increasing shear strength profiles. The footings’ uniaxial bearing capacities and failure surfaces under combined vertical, horizontal, and moment loading are reported. The results are analyzed in the context of application by the mobile jack-up industry, for which understanding of the circular spudcan footing’s bearing capacity under general loading is required for site-specific assessments. The paper also presents a parametric study on the effect of a footing’s aspect ratio (thickness/diameter) on its bearing capacity. To conclude, a closed...

The undrained bearing capacity of a spudcan foundation under combined loading in soft clay

Mobile jack-up drilling rigs are typically supported by individual, large diameter spudcan foundations. Before deployment, the suitability of a jack-up to a location must be shown in a site-specific assessment under loads associated with a 50-year return period storm, which ultimately need to be resisted by the foundations. The capacity of the spudcans under combined vertical, horizontal and moment loading is therefore integral to the overall site-specific assessment of the jack-up. In soft clays, spudcans can penetrate deeply into the seabed, sometimes up to several footing diameters, with soil flowing around the downward penetrating footing, sealing the cavity. Although this is generally believed to provide some additional bearing capacity to the footing, no detailed study or formal guidance is available to date. This study, therefore, investigates the influence of soil back-flow on the failure mechanisms and quantifies the effect on the capacity of a spudcan under general loading through finite element analyses. A closed-form analytical expression is developed that describes the capacity envelope under combined loading, applicable to embedment depths ranging from shallow to deep.

Undrained bearing capacity of spudcan under combined loading

The bearing capacities of spudcan foundation under pure vertical (V), horizontal (H), moment (M) loading and the combined loading are studied based on a series of three-dimensional finite element analysis. The effects of embedment ratio and soil non-homogeneity on the bearing capacity are investigated in detail. The capacities of spudcan under different pure loading are expressed in non-dimensional bearing capacity factors, which are compared with published results. Ultimate limit states under combined loading are presented by failure envelopes, which are expressed in terms of dimensionless and normalized form in three-dimensional load space. The comparison between the presented failure envelopes and available published numerical results reveals that the size and shape of failure envelopes are dependent on the embedment ratio and the non-homogeneity of the soil.

Undrained failure envelope for skirted foundations under general loading

Three-dimensional failure envelopes can be used to define the bearing capacity and proximity to failure of shallow foundations under general vertical, horizontal and moment loading (V, H, M/B). Different structures, and different load cases for the same structure, cover varying domains of (±V, ±H, ±M/B) load space; therefore, a fully encompassing failure envelope in (V, H, M/B) load space is a useful tool to define ultimate limit states for design. In this technical note, a closed-form expression is proposed that enables prediction of undrained bearing capacity of skirted foundations under general in-plane loading, valid for a range of embedment ratios and soil shear strength heterogeneities.

An upper-bound solution for the undrained bearing capacity of strip footings at the top of a slope

An analytical upper-bound plasticity solution is presented for the calculation of the undrained bearing capacity of strip footings on or near slopes. Typical results, presented in terms of the undrained bearing capacity factor, are shown to be in excellent agreement with finite-element analysis results and generally more conservative than those obtained from other available solutions. The proposed upper-bound solution is used to investigate the influence of the slope angle, the distance of the footing from the slope, the footing width and the soil properties on the undrained bearing capacity.

Penetration Resistance and Stiffness Factors for Hemispherical and Toroidal Penetrometers in Uniform Clay

This paper reports numerical analyses of shallowly embedded hemispherical and toroidal penetrometers under torsional and vertical load. These novel penetrometers are a new design suited to the assessment of near-surface soil strength and are aimed at the analysis of pipeline embedment and axial pipe-soil interaction. The geometry of the penetrometers avoids the complication of end effects that arise if a short pipe segment is used, as is the current practice. The operation of these devices involves vertical penetration typically of up to half a diameter, followed by rotation about the vertical axis, whereas the corresponding loads are recorded. The FE analyses explore the undrained bearing capacity and stiffness factors required for the measured loads to be converted to soil strength and stiffness for application in design. On the basis of these analyses, the geometry of the toroidal penetrometer has been optimized to minimize the size of the instrument and limiting interference across the toroid, which would hamper comparisons between the penetrometer response and a pipeline. It is shown that a relatively compact toroid can be used.

The influence of load inclination on the undrained bearing capacity of strip footings on slopes

The effect of inclined loading on the bearing capacity of foundations on horizontal ground surface is well established and both the exact solution and simpler empirical equations are available for the calculation of the failure loads. However, for footings on or near slopes complete solutions are available only for vertical loading. This paper investigates the influence of inclined loading on the horizontal and vertical failure loads. The finite element, upper bound plasticity and stress field methods are used to examine a wide range of geometries and soil properties. The methods are first validated against known solutions for two special cases and are subsequently employed to investigate the effect of the geometrical and material properties on the failure loads and the bearing capacity load interaction diagram. Based on this investigation an empirical equation is proposed for the load interaction diagram for undrained inclined loading of footings on or near slopes.

Undrained Bearing Capacity of Strip Footings on Slopes

The undrained bearing capacity of foundations on or near slopes is commonly calculated using empirical equations or from design charts which have been produced based on limit equilibrium or upper bound plasticity calculations. Many of the available methods do not take account of important parameters that affect the undrained bearing capacity factor, such as the distance of the footing from the slope, the slope height, or the soil properties. This paper presents finite element analyses of strip footings on or near undrained soil slopes performed in order to investigate the influence of the various parameters that affect undrained bearing capacity. The results of the analyses are compared to available methods. It is found that while some of these methods compare well with the finite element results for certain combinations of geometrical parameters and soil properties, they cannot produce sufficiently accurate results as they either do not take account of all of the affecting parameters or are generally not conservative. Based on the finite element results, design charts, equations, and a design procedure are proposed for the calculation of the undrained bearing capacity factor N c as a function of the undrained shear strength and the bulk unit weight of the soil, the footing width, the distance of the footing from the slope, the slope angle and the slope height.

Effect of embedment on the undrained capacity of shallow foundations under general loading

Results of a finite element study addressing the effect of embedment on the undrained bearing capacity of shallow strip foundations under uniaxial and combined loading are reported. Uniaxial vertical (V), moment (M) and horizontal (H) capacity and combined VH, VM and general VMH capacity are assessed. Ultimate limit states and the kinematic mechanisms accompanying failure are presented. Ultimate limit states under combined loading are presented as failure envelopes expressed in terms of loads non-dimensionalised by the foundation geometry and soil undrained shear strength and loads normalised by the ultimate uniaxial limit load, in order to describe their size and shape respectively. The results presented in this paper show that the size and shape of failure envelopes defining the undrained capacity of shallow foundations under general loading are dependent on embedment ratio.

Rate effects on the vertical uplift capacity of footings founded in clay

This paper describes results from a series of uplift tests performed in a drum centrifuge on shallow square footings founded on clay and sand, with an overlying sand backfill. The test series investigated footings of various widths loaded at displacement rates extending over five orders of magnitude. Additional tests were performed to examine the influence on uplift capacity of the direction of load inclination. The uplift tests performed on footings founded on sand enabled estimations to be made of the suction that developed at the base of the footings founded on clay. It is shown that the suction mobilised at very fast rates may be assessed using existing undrained bearing capacity approaches and a (rate corrected) operational undrained strength similar to that measured in triaxial extension. The uplift rates required to reach fully undrained conditions are almost two orders of magnitude higher than those for footings loaded in compression, and the upward footing displacements required to generate maximum resistance can be up to 10% of the footing width. These findings have important implications for shallow foundations such as those used to support high-voltage electricity transmission line support structures.

Two- and three-dimensional bearing-capacity solutions for footings on two-layered clays

In this paper, finite element analysis is used to predict the undrained bearing capacity of strip, square and circular footings resting on layered clays. The soil profile consists of two clay layers with different thicknesses and properties. The results are compared with previous solutions for strip footings on layered clays. The bearing-capacity behaviour is discussed and the bearing-capacity factors are given for various cases involving a range of layer thicknesses and properties of the two clay soil layers.

Depth factors for undrained bearing capacity

Depth factors for undrained bearing capacity

A spudcan foundation model with excess pore pressures. Part 1. A principle of effective loads

One of the challenges for the development of plasticity models for footings is to incorporate the special conditions of undrained and drained responses into a single model which also caters for intermediate conditions of partial drainage. By analogy with Terzaghi's Principle of Effective Stress, this paper proposes a Principle of Effective Loads for modelling the behaviour of a spudcan footing on saturated soil. Part 1 of the paper explores the principle for vertical loading. Consistent interpretations are developed for drained and undrained bearing capacity, and for tension capacity. A possible cause of unexpectedly rapid penetration during preloading is identified. Part 2 of the paper will use these interpretations and results to develop a model of excess pore pressure effects under combined ( V, H, M) loading.

Effects of long-term pre-loading on the performance of a footing on clay

An instrumented footing test in Bothkennar clay is described, which examines the effects of a long period of drained pre-loading on the footing's undrained bearing capacity. It is seen that pre-loading induced a significant increase in the subsequent foundation stiffness due to consolidation but also due to creep and ageing processes that led to an outward expansion of the clay's large-strain yield surface. Pre-loading also resulted in a downward shift of the bearing capacity mechanism and an ultimate bearing capacity that was substantially greater than that expected due to consolidation effects alone. Evolving anisotropy and creep are identified as being important contributory factors to the enhanced undrained capacity after pre-loading.

Effects of long-term pre-loading on the performance of a footing on clay

An instrumented footing test in Bothkennar clay is described, which examines the effects of a long period of drained pre-loading on the footing's undrained bearing capacity. It is seen that pre-loading induced a significant increase in the subsequent foundation stiffness due to consolidation but also due to creep and ageing processes that led to an outward expansion of the clay's large-strain yield surface. Pre-loading also resulted in a downward shift of the bearing capacity mechanism and an ultimate bearing capacity that was substantially greater than that expected due to consolidation effects alone. Evolving anisotropy and creep are identified as being important contributory factors to the enhanced undrained capacity after pre-loading.

Numerical Study of the Effect of Preloading on Undrained Bearing Capacity

In practice the situation often arises where extra load needs to be added onto existing foundations. This can arise due to the installation of additional equipment in a building, or to the construction of new floors, etc. It also arises in a situation where old foundations are used for a new building, a practice likely to become increasingly popular in the future. If the foundation soil is clay, then its undrained strength would have increased with time due to the dissipation of excess pore water pressures generated during the initial construction of the foundations. The design problem is determining how large this increase in undrained strength is, since this will determine the amount of new load that can be applied. This paper provides guidelines to answering this question through a numerical study of preloaded surface footings on both soft and stiff clay foundations. Additional information resulting from this study addresses the footing failure mechanisms, as well as the effect of a surface crust in so...

Undrained bearing capacity factors for conical footings on clay

Undrained bearing capacity factors for conical footings on clay

Undrained bearing capacity factors for conical footings on clay

INTRODUCTION The bearing capacity of circular foundations on undrained clay is of fundamental importance in many geotechnical problems. In particular there are a number of designs of offshore foundations where the foundation can be treated approximately as a large circular footing, for instance some gravity bases, the spudcan foundations of jack-up units, and the more recently developed caisson foundations. In most cases the footing is not placed at the ground surface, and it is important to take into account the depth of embedment. Furthermore, the base of a spudcan is generally not flat, but approximates a shallow cone. For foundations on soft clays, the effect of the increase of strength of the soil with depth needs to be taken into account, and this is particularly important for large foundations. The purpose of this note is to present calculations of bearing capacity factors for shallow circular foundations, accounting for embedment, cone angle, rate of increase of strength with depth, and surface roughness of the foundation. The results have widespread application, particularly in the offshore industry. The soil is assumed to be rigid-plastic, with yield determined by the Tresca condition with an undrained strength su. The method of characteristics is used for the bearing capacity calculation, as described by Shield (1955), Eason & Shield (1960), Houlsby (1982) and Houlsby & Wroth (1982a) for application to undrained axisymmetric problems. Some previous results have been published for this problem using similar numerical techniques (e.g. Houlsby & Wroth, 1982b; Salencon & Matar, 1982; Houlsby & Wroth, 1983; Tani & Craig, 1995; Martin, 2001), but the study presented here involves a much more comprehensive coverage of the parameters. Where comparisons can be made with the previous solutions, the factors differ by up to about 0·5%, which gives some indication of the level of accuracy attainable with this numerical technique. Exceptionally, the rough footing results given by Tani & Craig (1995) are higher by up to about 5%, but this may be due to a problem with their numerical integration procedures (see Martin & Randolph, 2001).